MODEL QUESTION PAPER FOR 2023-24

I PUC - PHYSICS (33)

Time: 3 hours 15 min. Max Marks: 70
General Instructions:
1. All parts are compulsory.
2. For Part – A questions, first written-answer will be considered for awarding marks.
3. Answers without relevant diagram / figure / circuit wherever necessary will not carry any marks.
4. Direct answers to the numerical problems without detailed solutions will not carry any marks.
Harish Shastry-9480198001
PART – A
I. Pick the correct option among the four given options for ALL of the following
questions: 5x1 = 15

1. Select the number with 3 significant figures

(A) 3.000 (B) 03.000 (C) 02.00 (D) 003.000

2. V-t graphs of four different particles are given. Which particle is under
retardation?

3. A vector is multiplied by a negative integer. Now,

(A) both magnitude and direction of the original vector are altered
(B) only magnitude of original vector changes while direction remains the same
(C) Only direction of original vector changes while magnitude remains the same
(D) Both the magnitude and direction of original vector remain the same.

4. Aristotle’s fallacy was corrected by

(A) Newton (B) Kepler (C) Galileo (D) Kelvin

5. Two different surfaces are in contact. Component of contact force parallel to the
surfaces is called
(A) normal reaction (B) frictional force
(C) Gravitational force (D) upthrust

6. One horsepower is equal to

(A) 1kW (B) 100kW (C) 1000kW (D) 746W

7. Dimension of moment of inertia is

(A) [MLT-2] (B) [ML2T-2] (C) [MoLT-2] (D) [ML2TO]

8. According to Kepler, all planets move round the sun

(A) in elliptical orbit (B) in straight lines
(C) in parabolic path (D) hyperbolic path
9. Buckling can be reduced by
(A) increasing the depth of the beam
(B) decreasing the depth of the beam
(C) increasing the length of the beam
(D) decreasing the breadth of the beam

10. If the angle of contact between glass and a liquid is acute, then
(A) liquid level rises in capillary tube of glass
(B) liquid level falls in capillary tube of glass
(C) liquid level inside the capillary tube remains in the same level as outside liquid.
(D) capillary rise/fall doesn’t depend on angle of contact.

11. A large ice block at 0oC is put inside a calorimeter containing water at 30oC. Now,
(A) temperature of 0oC ice increases.
(B) temperature of 30oC water rises
(C) temperature of 0oC ice decreases
(D) temperature of 30oC water decreases.

12. Below are two statements. Read the statements and select the correct option.
Statement I : Pressure of an ideal gas is doubled during an isochoric process. Work
done by the is found to be zero.
Statement II : Work done during isochoric process is zero.
(A) Statement I is wrong but the statement II is correct.
(B) Statement I is correct but the statement I is wrong
(C) Both statements I and II are correct and Statement II is the correct explanation for
statement I
(D) Both statements I and II are correct but the statement II is not the correct explanation
for statement I

PV
13. For one mole of an ideal gas, the equation is = x . P is pressure, V is volume and
R
R is universal gas constant. X represents…….
(A) mass of the gas (B) temperature of the gas
(C) specific heat at constant pressure (D) ratio of specific heats

14. A motion that repeats itself at regular intervals of time is called

(A) uniform motion (B) two-dimensional motion
(C) accelerated motion (D) periodic motion

15. In a stationary wave formation, the point where particles vibrate with maximum
amplitude is called
(A) crest (B) trough (C) node (D) Antinode

II Fill in the blanks by choosing appropriate answer given in the brackets for ALL the
following questions: 5×1=5
(Henry Cavendish, Avogadro, in gases, perpendicular, at the sea level,)
16. When a stone is whirled in a circular path using a string with uniform speed, its direction
of velocity and acceleration are …………… to each other.
17. The scientist who determined the value of universal gravitational constant is ……..
18. At a point, a student measures atmospheric pressure and records it as P=1.013×105Pa. He
is …………..
19. Equal volumes of all gases at equal temperature and pressure have the same number of
molecules. This hypothesis was proposed by………
20. Transverse mechanical waves cannot travel ……….

PART – B
II. Answer any FIVE of the following questions: 5 × 2 = 10
2
21. Show that the equation x=vot + ½ at is dimensionally correct. Symbols have usual
meaning.
22. Define unit vector. Write the unit vector of A = 8iˆ + 6jˆ .
23. Write any two advantages of friction.
24. What is a conservative force? Given an example for conservative force.
25. Define centre of mass. Write an expression for centre of mass of a system of particles
lying along x-axis.
26. How does acceleration due to gravity vary with depth from the surface? What is the
acceleration due to gravity at the centre of the earth?
27. What is anomalous expansion of water? How does this property of water help in
protecting animal and plant life inside water?
28. State and explain first law of thermodynamics
29. What are the properties of a particle executing SHM?

PART – C
III. Answer any FIVE of the following questions: 5 × 3 = 15
30. What is a projectile? What is the trajectory of a projectile? Give an example for a
projectile.
31. State and explain law of conservation of linear momentum.
32. Write an expression for work done by a force. Write two conditions in which work done
is zero.
33. An acrobat of moment of inertia 100kg m2, rotating at a speed of 12rpm, suddenly
reduces the moment of inertia to 50kgm2 by folding the arms. What is the new rotational
frequency (in rpm) after folding hands?
34. Draw a typical stress strain graph and mention the elastic limit in the graph.
35. State Pascal’s law. Write any two applications of Pascal’s law.
36. What is conduction? On what factors does the flow heat in a conductor depend?
37. Define molar specific heat at constant volume (CV) and constant pressure (Cp). What is
Cp - CV =?
38. Write any three properties of sound waves.

PART – D
IV. Answer any THREE of the following questions: 3 × 5 = 15

39. Derive the equation v2=vo2 + 2ax using v-t graph. Symbols have usual meaning.
40. What is centripetal acceleration? What is its direction? Obtain an expression for the
centripetal acceleration of a particle moving with uniform speed in a circular path.
41. Define spring force. Assuming the expression for spring force and using force -
displacement graph obtain an expression for potential energy of a spring.
42. (a) Define torque. (1)
(b) Explain the principle of moments of a lever (4)
43. (a) What is Carnot cycle? (1)
(b) Draw the PV diagram of Carnot’s Cycle. (2)
(c) Write the expression for efficiency of Carnot’s cycle and explain the terms (2)
44. Obtain an expression for the velocity of a transverse wave in a stretched wire in terms of
tension and mass per unit length of the wire.

V. Answer any TWO of the following questions: 2 × 5 = 10

45. A particle starts from the origin at t = 0 s with a velocity of (4 î +3 ĵ ) ms-1. The body
moves in the x-y plane with a constant acceleration of a = −10ˆj ms-2. Find (a) the
maximum height (b) range and (c) time of flight of the projectile.
46. Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a
horizontal table. What is the gravitational force and potential at the mid point of the line
joining the centres of the spheres?
47. A brass boiler has a base area of 0.15 m2 and thickness 1.0 cm. It boils water at the rate
of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part of the
flame in contact with the boiler. Thermal conductivity of brass = 109 J s–1 m–1 K–1 ; Heat
of vaporisation of water = 2256 × 103 J kg–1 .
48. A spring having with a spring constant 1200 N m–1 is mounted on a horizontal frictionless
table. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled
sideways to a distance of 2.0 cm and released. Determine (i) the frequency of oscillations,
(ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.

*********
 Answers to few questions

PART – A

1. Select the number with 3 significant figures

(A) 3.000 (B) 03.000 (C) 02.00 (D) 003.000

2. V-t graphs of four different particles are given. Which particle is under
retardation?

Answer C
3. A vector is multiplied by a negative integer. Now,
(A) both magnitude and direction of the original vector are altered
(B) only magnitude of original vector changes while direction remains the same
(C) Only direction of original vector changes while magnitude remains the same
(D) Both the magnitude and direction of original vector remain the same.

4. Aristotle’s fallacy was corrected by

(A) Newton (B) Kepler (C) Galileo (D) Kelvin

5. Two different surfaces are in contact. Component of contact force parallel to the
surfaces is called
(A) normal reaction (B) frictional force
(C) Gravitational force (D) upthrust
6. One horsepower is equal to
(A) 1kW (B) 100kW (C) 1000kW (D) 746W
7. Dimension of moment of inertia is
(A) [MLT-2] (B) [ML2T-2] (C) [MoLT-2] (D) [ML2TO]
8. According to Kepler, all planets move round the sun
(A) in elliptical orbit (B) in straight lines
(C) in parabolic path (D) hyperbolic path
9. Buckling can be reduced by
(A) increasing the depth of the beam
(B) decreasing the depth of the beam
(C) increasing the length of the beam
(D) decreasing the breadth of the beam
10. If the angle of contact between glass and a liquid is acute, then
(A) liquid level rises in capillary tube of glass
(B) liquid level falls in capillary tube of glass
(C) liquid level inside the capillary tube remains in the same level as outside liquid.
(D) capillary rise/fall doesn’t depend on angle of contact.
11. A large ice block at 0oC is put inside a calorimeter containing water at 30oC. Now,
(A) temperature of 0oC ice increases.
(B) temperature of 30oC water rises
(C) temperature of 0oC ice decreases
(D) temperature of 30oC water decreases.
12. Below are two statements. Read the statements and select the correct option.
Statement I : Pressure of an ideal gas is doubled during an isochoric process. Work
done by the is found to be zero.
Statement II : Work done during isochoric process is zero.
(E) Statement I is wrong but the statement II is correct.
(F) Statement I is correct but the statement I is wrong
(G) Both statements I and II are correct and Statement II is the correct explanation for
statement I
(H) Both statements I and II are correct but the statement II is not the correct explanation
for statement I
PV
13. For one mole of an ideal gas, the equation is = x . P is pressure, V is volume and
R
R is universal gas constant. X represents…….
(A) mass of the gas (B) temperature of the gas
(C) specific heat at constant pressure (D) ratio of specific heats
14. A motion that repeats itself at regular intervals of time is called
(A) uniform motion (B) two-dimensional motion
(C) accelerated motion (D) periodic motion
15. In a stationary wave formation, the point where particles vibrate with maximum
amplitude is called
(A) crest (B) trough (C) node (D) Antinode

II Fill in the blanks by choosing appropriate answer given in the brackets for ALL the
following questions: 5×1=5
16. When a stone is whirled in a circular path using a string with uniform speed, its direction
of velocity and acceleration are perpendicular to each other.
17. The scientist who determined the value of universal gravitational constant is Henry
Cavendish.
18. At a point, a student measures atmospheric pressure and records it as P=1.013×105Pa. He
is at the sea level.
19. Equal volumes of all gases at equal temperature and pressure have the same number of
molecules. This hypothesis was proposed by Avogadro
20. Transverse mechanical waves cannot travel in gases.

PART – B
22. A vector of magnitude unity is called unit vector.
A = 8iˆ + 6jˆ .
A = 82 + 62 = 10
A 8iˆ + 6ˆj
 = = = 0.8iˆ + 0.6ˆj
A 10
38. An acrobat of moment of inertia 100kg m2, rotating at a speed of 12rpm, suddenly
reduces the moment of inertia to 50kgm2 by folding the arms. What is the new rotational
frequency (in rpm) after folding hands?
According to conservation of angular momentum, I1ω1 = I2ω2
100 x 12 = 50 x ω2
ω2 = 24rpm
 Given mass number of iron nucleus as A=56, what is the volume of iron nucleus?
Ro=1.2x10-15m.
Answer: R=RoA1/3
4 4 1
Volume of the nucleus, V = πR 3 = π(R o A 3 )3
3 3
4 4
V = πR 3o A = π(1.2x10−15 )3 x56  V= 4.05x10-43 m3
3 3

45. A particle starts from the origin at t = 0 s with a velocity of (4 î +3 ĵ ) ms-1. The body
moves in the x-y plane with a constant acceleration of a = −10ˆj ms-2. Find (a) the
maximum height (b) range and (c) time of flight of the projectile.
V 2 sin 2 θ V 2 sin 2θ 2V sin θ
Formula: H = o : R= o : T= o
2g g g

Here Vo = v2x + v2y = 42 + 32 = 5ms −1

3 4
From the diagram, sin θ = and cos θ =
5 5
( )
2
2 3
5
Maximum height, H = 5 = 25x9 = 0.45m
2x10 20x25
3 4
52 x2x  x 
V sin 2θ Vo 2sin θ cos θ
2 2
 5 5  = = 25x2x12 = 2.4m
Range, R = o = =
g g 10 10x25
3
2x5x
2V sin θ 5 = 0.6s
Time of flight, T = o =
g 10
46. Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a
horizontal table. (a) What is the gravitational force between them? (b) What is net
gravitational field at the centre of the line joining the spheres? (c) What is the potential
at the mid-point of the line joining the centres of the spheres?
 m1m 2 GM
Formula: F = G 2
: V=−
r r

100x100
(a) F = 6.67x10−11 = 6.67x10−7 N
12
(b) If an object is kept at the centre, it will experience equal and opposite force due to
both the spheres. Hence net force and net field at the centre is zero.
GM1  GM 2 
(c) Vnet = − +− 
r  r 
6.67x10−11 x100
Vnet = −2x = −26.68x10−9 Jkg −1
0.5

47. A brass boiler has a base area of 0.15 m2 and thickness 1.0 cm. It boils water at the rate
of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part of the
flame in contact with the boiler. Thermal conductivity of brass = 109 J s–1 m–1 K–1 ; Heat
of vaporisation of water = 2256 × 103 J kg–1 .
KA(θ1 − θ 2 )t
Formula: Q = : Q=mL
KA(θ1 − θ 2 )t
mL =
109x0.15(θ1 − 100)x60
6x2256x103 =
1x10−2
6x2256x103 x10−2
= (θ1 − 100)
109x0.15x60
137.98 = (θ1 −100)
θ1 = 237.98o C

48. A spring having with a spring constant 1200 N m–1 is mounted on a horizontal frictionless
table. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled
sideways to a distance of 2.0 cm and released. Determine (i) the period and angular
frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum
speed of the mass.

m
Formula: T = 2π : amax = -2A : vmax=-A
k
3 1
(i) T = 2π = 2x3.14x = 0.314sec
1200 20

k 1200
ω= = = 20 rad sec−1
m 3
amax = -2A  a max = − ( 20 ) x2x10−2 = −8ms −2
2
(ii)
(iii) vmax=-A  v max = − ( 20 ) x2x10 −2 = −0.4ms −1
 CHRIST KING PU COLLEGE, KARKALA
PREPARATORY EXAMINATION - I (JANUARY - 2023)
CLASS : I PUC TIME: 3 : 15 MINUTES
DATE : 27/01/2024 SUBJECT : PHYSICS MARKS :70
Instruction:
(i) All parts are compulsory.
(ii) Part – A questions have to be answered in the first two pages of the answer – booklet.
For Part – A questions, first written – answer will be considered for awarding marks.
(iii) Answer without relevant diagram / figure / circuit wherever necessary will not carry marks.’
(iv) Direct answers to Numerical problems without detailed solutions will not carry any marks.
==============================================================================
PART – A
I Pick the correct option among the four options for ALL of the following questions. 15 x 1 = 15
1. The number of significant figures in 0.001020 m.
a) 3 b) 4 c) 6 d) 7
−1
2. The acceleration of a particle moving with uniform velocity 10 𝑚𝑠 for 2 s is
a) 10 𝑚𝑠 −2 b) 5 𝑚𝑠 −2 c) 0 d) 20 𝑚𝑠 −2
3. Expression for centripetal acceleration of a particle moving with uniform speed v and in a
circular path radius r is
𝑣 𝑣2
a) 𝑎 = 𝑣 2 𝑟 b) 𝑎 = 𝑣 2 𝑟 2 c) 𝑎 = 𝑟 2 d) 𝑎 = 𝑟
4. Dust in a duster cleaned by hitting it on wall or ground. Dust removed out of duster due to
a) Inertia of rest b) Inertia of motion
c) Kinetic energy of particle increase d) Kinetic energy of particle decreases
5. The commercial unit of electrical energy equal to
a) Kilowatt b) Horse power c) Kilowatt hour d) Joule
6. Dimensional formula for which of the following pair of physical quantities are same?
a) Work & power b) Angular momentum & kinetic energy
c) Torque & work d) Angular momentum & force
7. The period of revolution of Geo stationery satellite equal to
a) one day b) one week c) one month d) one year
8. Young’s modulus is inversely proportional to
a) Lateral strain b) Bulk modulus c) Longitudinal stress d) Longitudinal strain
9. The instrument used to measure Gauge pressure is
a) Thermometer b) Open tube manometer c) Multi meter d) Barometer
10. Example for Convection mode of heat transfer is
a) Land breeze b) Trade wind
c) Sea breeze d) All the 3 options A, B and C are correct
11. The body temperature of normal human beings equal to 37 0 𝐶 . Body temperature of normal
human beings in Fahrenheit scale to
a) 98.6 0 𝐹 b) 310 0 𝐹 c) 37 0 𝐹 d) 103.6 0 𝐹
12. ∆𝑄 - Heat energy supplied to a system, ∆𝑈 - increase in internal energy and ∆𝑊 = 𝑃∆𝑉 -
work done by system then, the correct relation for isochoric process is
a) ∆𝑄 = ∆𝑈 + 𝑃∆𝑉 b) ∆𝑄 = ∆ 𝑃∆𝑉 c) ∆𝑄 = ∆𝑈 d) ∆𝑄 = ∆𝑈 + ∆𝑊
13. The real gases approach ideal gas behaviour at
a) Low pressure and high temperature b) High pressure and high temperature
c) High pressure and low temperature d) Low pressure and low temperature
 14. Planets rotates about their own axis and revolve around Sun, their motion is
a) Periodic and Oscillatory b) Not periodic and not oscillatory
c) Periodic but not Oscillatory d) Simple Harmonic motion
15. Electromagnetic waves are
a) Longitudinal requires medium for their propagation
b) Longitudinal do not require any medium for their propagation
c) Transverse do not require any medium for their propagation
d) Transverse requires medium for their propagation
II Fill in the blanks by choosing appropriate answer given in the brackets for ALL the
following questions. 5x1=5
(Isothermal, number density, Pascal’s law, Poles, law of conservation of momentum)
16. “When net force acting on system equal to zero, total linear momentum of system is
conserved”. This statement is ___________
17. Acceleration due to gravity on earth at ____________ is greater than that in equator.
18. Hydraulic lift work according to _____________
19. The mean free path of a gas molecule is inversely proportional to __________
20. According to Newton, the propagation of sound in air is ________ process.

PART – B
III Answer any FIVE of the following questions. 5 x 2 = 10
21. Write the two differences between speed and velocity.
22. Define: i) null vector and ii) unit vector
23. Define elastic and inelastic collisions.
24. Write the expression for acceleration due to gravity at depth d from earth surface and mention
the terms.
25. State i) Zeroth law and ii) First law of thermodynamics.
26. State and explain law of equipartition of energy.
27. Write the equation of path of the projectile. Give its name.
28. Mention the expression for mean free path. Explain the terms.
29. List the two differences between transverse wave and longitudinal wave.
PART – C
IV Answer any FIVE of the following questions. 5 x 3 = 15
1
30. Check the correctness of equation, ∆𝑥 = 𝑣0 + 2 𝑎𝑡 2 using dimensional analysis.
31. Find the magnitude of resultant of two vectors acting by making an angle 𝜃 between them.
32. List any two advantages and one disadvantage of friction.
33. A police officer fires a bullet of mass 0.05kg with kinetic energy of 1000 J on a soft ply wood.
It emerges with 10% of its initial kinetic energy. What is the emergent speed of the bullet?
34. State law of conservation of angular momentum. Give two examples.
35. Define Young’s modulus. Write the expression for Young’s modulus of the material of a wire
and explain the terms.
36. Distinguish between stream line flow and turbulent flow of fluids.
37. Show that for an ideal gas coefficient of volume expansion at constant pressure is inversely
1
proportional to temperature. 𝛼𝑉 = 𝑇

38. Write the displacement relation (equation) of a progressive wave travelling in the negative
direction of x – axis with initial phase Φ. Explain the terms.
 PART – D
V Answer any THREE of the following questions. 3 x 5 = 15
39. What is velocity – time graph? Derive 𝑣 2 = 𝑣02 + 2𝑎𝑥 using v – t graph.
40. State Newton’s second law of motion. Derive 𝐹 = 𝑚𝑎.
41. Illustrate the law of conservation energy for a freely falling body of mass m and falling from
height H.
42. i) State Kepler’s law of orbit of planetary motion. 1
ii) State and explain Kepler’s law of area of planetary motion. 2
iii) State and explain Kepler’s law of periods of planetary motion. 2
43. Derive an expression for work done in an isothermal process.
44. i) Derive an expression for potential energy of a particle executing SHM 3
ii) At what positions potential energy of a particle executing SHM is maximum and minimum?2
VI Answer any TWO of the following questions. 2 x 5 = 10
45. A solid cylinder of mass 20 kg rotates about its axis with angular speed of 100 𝑟𝑎𝑑𝑠 −1 . The
radius of cylinder is 0.25 m.
a) What is the kinetic energy associated with rotation of the cylinder?
b) What is the magnitude of momentum of cylinder about its axis?
46. A wave travelling along a string described by 𝑦 𝑥, 𝑡 = 0.005 sin 80.0𝑥 − 3.0𝑡 , in which
numerical constants are in S.I. units. Calculate
a) Amplitude b) Period of wave c) Frequency
d) Wavelength and e) Speed of propagation of wave
47. A stone tied to the end of string 1 m long is whirled in a horizontal circle with a constant
speed. If the stone makes 150 revolution in 25 seconds. What is the magnitude and direction of
acceleration of the stone?
48. Calculate the rate of flow of heat through a glass window 2.0 m X 1.5 m area and 3.2 mm
thick. If the temperature of inner and outer surfaces are 150 𝐶 and 140 𝐶 respectively (K for
glass = 0.84 𝑊 𝑚−1 𝐾 −1 ).

*************************
 ST. ANTHONY’S PU COLLEGE
RV COLLEGE POST, MYSORE ROAD, BANGALORE – 560059

PREPARATORY EXAMINATION, JAN 2024

SUBJECT: I PUC PHYSICS (33)

TOTAL NUMBER OF QUESTIONS: 48

DURATION: 3Hrs 15 Min MAX∙MARKS: 70

General Instructions:
a) All parts are compulsory.
b) Part – A questions have to be answered in the first two pages of the answer-booklet. For Part
– A questions, first written-answer will be considered for awarding marks.
c) Answers without relevant diagram / figure / circuit wherever necessary will not carry any
marks.
d) Direct answers to the numerical problems without detailed solutions will not carry any marks.

PART – A
I. Pick the correct option among the four given options for all of the following questions
15× 1 = 15
1. The number of significant figures in 0.1230 m is
a] One b] Two c] Three d] Four
2. The slope of position – time graph gives
a] Acceleration b] Position c] Displacement d] Velocity
3. An example of scalar quantity is
a]Displacement b]Speed c]Velocity d]Torque
4. Inertia of an object is quantitative measure of its:
a]Volume b]Density c]Mass d]Temperature
5. When a body is thrown vertically upwards, work done by gravity is
a]Positive b]Zero c]Negative d]Can’t predict
6. The angular acceleration of a body is directed
a] Towards the center of the circle b] Away from the center of the circle
c] Along the tangent to the circle d] Along the axis of rotation
7. The period of revolution of Geo stationery satellite equal to
a]One month b] One week c] One day d] One year
8. Young’s modulus of elasticity of a perfectly rigid body is
a] Unity b] Infinity c] Zero d] None of these
9. Turbulent flow is:
a] Unsteady and regular b] Steady and irregular
b] Irregular d] Regular
 10. The amount of heat conducted through a metal rod is directly proportional to
a] Temperature gradient b] Area of cross section
c] Time during which heat flows d] All of these
11. Land breeze is an example for:
a] Thermal conduction b] Thermal radiation
c] Natural convection d] Black body radiation
12. The significance of first law of thermodynamics is
a] Law of conservation of mass b] Law of conservation of momentum
c] Law of conservation of energy d] Law of conservation of angular momentum.
13. Ratio of specific heat for a diatomic gas is
a] 7 / 5 b] 5 / 3 c] 9 / 7 d] 8 / 6
14. The time period of second’s pendulum is
a] 2 s b] 1 s c] 3 s d] 4 s
15. The longitudinal wave can propagate through
A]Solid only b]liquid only c]gas only d] solid, liquid and gas

II. Fill in the blanks by choosing appropriate answer given in the brackets for ALL the
following questions 5×1=5
(Adiabatic process, Directly, Decreases, Poles, Momentum)
16. Recoiling of gun explains law of conservation of ………………….
17. Acceleration due to gravity on earth at ………… is greater than that in equator.
18. Viscosity of liquid ……………..with temperature.
19. Average kinetic energy of gas is ……………….proportional to temperature of the gas.
20. According to Laplace, the propagation of sound in air is …………………

PART – B
III. Answer any five of the following questions 5 × 2 = 10
21. Write the dimensional formula for 1] Density and 2] Momentum.
22. Distinguish between path length and displacement.
23. State and explain triangular law of vector addition.
24. Show that P = ⃗F ∙ v
⃗ where the symbols have their usual meaning.
25. Give the general conditions of equilibrium of a rigid body.
26. State and explain Newton’s law of gravitation.
27. State and explain first law of thermodynamics.
28. Write an expression for ratio of specific heats in terms of degrees of freedoms a gas
molecule and explain the terms.
29. Mention any two characteristics of simple harmonic motion.

PART - C
IV. Answer any five of the following questions 5 × 3 = 15
30. Write the three uses of dimensional analysis.
31. Derive the expression for centripetal acceleration.
32. State the laws of friction.
 33. Prove work – energy theorem for a constant force.
34. Compare rotational motion and linear motion.
35. Draw typical stress – strain curve and mention yield point and fracture point.
36. Derive an expression for pressure exerted by the liquid.
1
37. Show that αV = for volume expansion.
T
38. Show that the overtones in a closed pipe are odd harmonics of the fundamental frequency.
PART - D
V. Answer any three of the following questions 3 × 5 = 15
1
39. What is v – t graph? Derive s = ut + 2 at 2 using v − t graph.
40. Derive an expression for maximum speed of a car on a banked circular road taking friction
into account.
41. State and prove law of conservation of mechanical energy in the case of a freely falling body.
42. a] What is escape velocity?
b] What is satellite?
C ] State Kepler’s laws of planetary motion.
43. What is an isothermal process? Derive an expression for work done in an isothermal
process.
44. a ]When is the velocity of a particle executing simple harmonic motion is maximum?
b] What is periodic motion? Give an example.
c] Define the terms: a) Time period and b) Frequency of oscillation.

VI. Answer any two of the following questions 2 × 5 = 10

45. A projectile is launched in to space at an angle of 60° with an initial speed of 200 ms—1 .
Calculate 1) maximum height, 2) time of flight and 3) range of projectile (g = 9.8 ms −2 )
46. The moment of inertia of a grindstone about its axis of rotation is 25 kgm2. Starting from
rest, it acquires a speed of 120 rpm in 10 seconds. Find the torque acting on it.
47. A thermocole ice box is a cheap and efficient method for storing small quantities of cooked
food in summer in particular. A cubical box of side 30cm has a thickness of 5cm. If 4kg of
ice is put in the box; estimate the amount of ice remaining after 6hrs. The outsid e
temperature is 45°C and coefficient of thermal conductivity of thermocole is 0.01J/s/m/K.
Heat of fusion of water = 335 × 103 J/kg.
t x
48. The equation for wave, y = 0.03 sin π (0.02 − 0.2 ) with the length expressed in metre and

time in second. Calculate the wave length, amplitude frequency and velocity of the wave

***** ALL THE BEST *****

 MODEL QUESTION PAPER 2023-24
I PU PHYSICS (33)
TIME:3HR 15MIN MAX MARKS:70
General Instructions:

1. All parts are compulsory.

2. For Part – A questions, first written-answer will be considered for awarding marks.
3. Answers without relevant diagram / figure / circuit wherever necessary will not carry any marks.
4. Direct answers to numerical problems without detailed solutions will not carry any marks.

PART – A
I. Pick the correct option among the four given options for ALL of the following
questions: 15X1=15

1. One nanometre is equal to

(A) 10 9 mm (B) 10 −6 cm (C) 10 −7 cm (D) 10 −9 cm
2. The velocity time graph of motion of an object starting from rest with uniform acceleration is a straight
line
(A). Parallel to time axis (B). Passing through origin
(C) Parallel to velocity axis (D). None of the above
3. If 𝐴⃗ + 𝐵 ⃗⃗ + 𝐴⃗ this shows that addition of vectors is
⃗⃗ = 𝐵
(A) Associative (B) Commutative (C) Additive (D) Additive inverse
4. Action and reaction forces act on
(A) The same body (B)The different bodies
(C) The horizontal surface (D)Nothing can be said
5 . Below are the two statements related to momentum
Statement I: If two objects of different masses have same momentum, the lighter body possesses
greater velocity.
Statement II : For all bodies momentum always remains same
(A) Both the statements I and II are correct and II is the correct explanation for I
(B) Both the statements I and II are correct and II is not the correct explanation for I
(C) Statement I is wrong but the statement II is correct
(D) Statement I is correct but the statement II is wrong
6. Work done in raising a box depends on
(A) How fast it is raised (B)The strength of the man
(C) The height by which it is raised (D)None of the above
7. Moment of inertia of a sphere of mass M and radius R is I. Keeping M constant if a graph is plotted
between I and R, then its form would be
I I I I

(A) (B) (C) (D)

R R R
R
8. Who among the following gave first the experimental value of G
(A) Cavendish (B) Copernicus (C)Brook Teylor (D)None of these
9 The modulus of elasticity is dimensionally equivalent to
(A)Surface tension (B) Stress (C)Strain (D)None of these
10. Hairs of shaving brush cling together when it is removed from water due to
(A) Force of attraction between hair (B)Surface tension
(C) Viscosity of water (D)Characteristic property of hairs
11. When vapour condenses into liquid
(A) It absorbs heat (B)It liberates heat
(C) Its temperature increases (D)Its temperature decreases
12. In which thermodynamic process, volume remains same
(A) Isobaric (B) Isothermal
(C) Adiabatic (D) Isochoric
13. The value of CV for one mole of neon gas is
(A) 1 R (B) 3
R (C) 5 R (D) 7 R
2 2 2 2

14. Acceleration of a particle, executing SHM, at it’s mean position is

(A) Infinity (B) Varies (C)Maximum (D)Zero
15. When a tuning fork vibrates, the waves produced in the fork are
(A) Longitudinal (B) Transverse (C)Progressive (D)Stationary
II. Fill in the blanks by choosing appropriate answer given in the bracket for ALL
the following questions: 5x1=5
(zero, decreases, elastic, antinodes, projectile, increases)
16. An object that is in flight after being thrown is called_______.
17. The force of attraction due to a hollow spherical shell of uniform density, on a point mass inside it is
______.
18. The viscosity of liquids ______ with temperature.
19. According to kinetic theory of gasses collision between the molecules are __________ in nature.
20. The points in a standing wave at which amplitude is maximum is called______.
PART – B
III. Answer any FIVE of the following questions: 5X2=10
21. Name any two derived SI unit with the name of scientist.
22. A vector having a magnitude of 15unit makes an angle 60°with the X axis. Find the horizontal and
vertical component?.
23. Mention two methods of reducing the friction.
24. What is non conservative force ? Give an example..
25. Give the general conditions of equilibrium of a rigid body.
26. Moon has no atmosphere. Why?
27. What is calorimetry? Give the principle of calorimetry.
28. What is a reversible process? Give an example.
29. Draw a graph of energy versus time in the case of a particle executing SHM.
PART – C
IV. Answer any FIVE of the following questions: 5X3=15
30. Define centripetal acceleration. Write the expression for it and explain the terms.
31. State Newton’s first law of motion and hence define force and inertia of a body
32. Prove work –energy theorem for a constant force.
33 The angular speed of a motor wheel is increased from 1200rpm to 3120 rpm in 16 seconds. What is its
angular acceleration, assuming the acceleration to be uniform ?
34. State Hooke’s law. Write two application of elastic behavior of the material.
35. Differentiate the streamline motion, turbulent motion and unsteady motion on the basis of Reynolds
number.
36. Show that the volume expansion coefficient at constant pressure for gases is equal to reciprocal of the
absolute temperature.
37. Explain kinetic interpretation of temperature.
38 Distinguish between longitudinal and transverse wave.
PART – D
V. Answer any THREE of the following questions: 3x5=15
t2
39. What is the velocity - time graph? Derive the equation of motion x = v0 t + ½ a using v-t graph.
40. Show that the trajectory of projectile is parabola.
41 State law of conservation of mechanical energy and illustrate the same in case of a freely falling body
42. a) Give the expression for moment inertia of a hollow cylinder of radius R about its axis. (1)
b) What is the relation between angular velocity and linear velocity (1)
c) Show that τ =Iα. Symbols have usual meaning. (3)
43. a) Explain the working of a Carnot's engine.(carnot cycle) (3)
b) What is an extensive variable? Give an example. (2)
44. What is closed pipe? Prove that the overtones in a closed pipe are odd harmonics.
VI. Answer any TWO of the following questions: 2x5=10
45. Two masses 7kg and 12kg are connected at the two ends of a light inextensible string that passes over a
pulley. Find the acceleration of the masses and the tension in the string.
46. A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 x108 km away
from the sun?
47. A body cools from 80 oC to 50 oC in 5 minutes. Calculate the time it takes to cool from 60 oC to 30 oC.
The temperature of the surrounding is 20 oC.
48. The acceleration due to gravity on the moon is 1.7m/s2. What is the time period of simple pendulum on
the moon if its time period on the earth is 3.5s.
 SAI NIKETAN
I PU PREPARATORY EXAMINATION 23-24

MARKS : 70 DURATION: 03 Hr 15 Min

SUBJECT: PHYSICS DATE : 27/01/2024

General Instructions:
1. All parts are compulsory.
2. For Part – A questions, first written-answer will be considered for awarding marks.
3. Answers without relevant diagram / figure / circuit wherever necessary will not carry any marks.
4. Direct answers to the numerical problems without detailed solutions will not carry any marks.

PART - A

I. Answer the following questions by choosing correct option out of given four options
(1X15 =15)
1. The order of the magnitude of number 11 is
a)10¹. b) 10². c) 10⁰. d) 10-1
2. Velocity time graph for uniform motion of a body is shown in figure. The displacement
of body in first 2 hours?.

a)50 km b) 100 km c) 25km d) 70km

3. The angle between two equal vectors is
a)0⁰. b) 60⁰. c) 90⁰. d) 180⁰
4. Action and reaction
a)acts on the same body. b) acts on two different bodies
c) cancel each other. d) are equal and acts in same direction
5. Change in the momentum is given by
a) Force x Mass. b) Force x Time
c) Force x velocity. d) Force x Distance
6. A light body and a heavy body have equal Kinetic energy. Which has the greater
momentum?
a)Heavy body. b) A light body.
c) both have same momentum. d) insufficient data.
 7. For which of the following does the centre of mass lie outside the body
a) Pencil. b) disc. c) bangle. d) shot-put
8. Force between two masses separated by some distance on earth is 3N. What is force
between same masses separated by same distance on moon?
a)3/2N. b) 2/3N c) 3N. d) 2N
9. Young’s modulus of wire depends on
a) it's length. b) it's area. c) it's material d) both a & b
10. Modulus of elasticity has dimension of
a) energy. b) power. c) pressure. d) torque
11. Liquid placed on glass does not wet the glass then angle of contact at the interface
between glass and liquid is
a)30⁰. b)60⁰. c) 0⁰. d)130⁰
12. Wien's displacement law used to determine the
a)mass density of stars. b) change in density of stars
c) radius of Stars. d) temperature of stars
13. Unit of spring constant is
a)dyne/cm. b) newton/meter. c) both a and b. d) none
14. Wave transport
a)matter. b) energy. c) both matter and energy. d) none
15. Internal energy of isolated system is
a) increases. b) decrease. c) remains same. d) none

II. Fill in the blanks with appropriate word given below (1X5=5)
(Antinode, 5, scalar,0, 180)
16.________ is point on standing waves at which amplitude is maximum
17. The degree of freedom of diatomic gas molecules at ordinary temperature is ______
18. Surface tension is ______ quantity
19. Coefficient of restitution for a perfectly inelastic collision is ______
20. Angle between negative vectors is ______ degree.

PART - B

III. Answer any following FIVE questions given below (2X5= 10)
21. Name the supplimetry quantities and their respective SI units.
22. Define. a) projectile b) Trajectory
23. Write any two disadvantages of friction.
24. What is power? Show that power P=F.V, where symbols have their usual meaning.
25. List any two characteristics of gravitational force.
 26. What do you mean by regelation of ice? Give one of it's practical example.
27. State first law of thermodynamics and write it's mathematical form.
28. Human heart beats 80 times in 60s. What is the frequency and time period of the heart
beat.

PART - C

IV. Answer any FIVE of the following questions. (3X5=15)

29. A projectile is fired with a velocity ‘u’ at an angle of  with the horizontal. Derive the
expression for maximum Height and time of flight of projectile.
30. State Newton’s II law of motion. And hence derive F=ma, where symbols have their
usual meaning.
31. A block of mass sliding with velocity 15m/s on rough surface, after sliding a distance
3m, it's velocity reduced to 7m/s. Find work done by friction.
32. What is rigid body? Mention condition for equilibrium of rigid body.
33. State Hook’s law. Draw the stress-strain diagram for ductile materials.
34. Derive expression for pressure at a point indside a liquid.
35. Distinguish between temperature and heat.
36. Define mean free path of a molecule of gas. Mention the factors on which mean free
path depends.
37. Distinguish between progressive and stationary waves.

PART - D

V. Answer any THREE of following questions (5 X 3= 15)

38. Plot v-t graph for uniformly accelerated motion of an object. Using this graph derive
equation s=ut+½ at²
39. State parallelogram law of vectors addition. Derive the magnitude and direction of the
resultant vector of two vectors acting at a point at angle of  with each other.
40. State and prove law of conservation of energy in case of freely falling body.
41. (a) Define torque
(b) write SI unit of torque
(c) derive the relation between torque and angular momentum.
42. (a) What is P-V diagram.
(b) draw the P-V diagram for isothermal process.
(c) derive the equation for work done during isothermal process.
43. Derive an expression for the total energy of a particle executing S.H.M
VI. Answer any TWO of following questions. (5X2=10)
44. A truck of mass 2x10⁴kg travelling at speed of 0.5 m/s collides with another truck of
half it's mass moving in opposite direction with velocity of 0.4 m/s. If the trucks couple
automatically on collision, calculate the common velocity with which they move.
45. At what height from the surface of earth will the value of g be reduced by 36% from
the value at the surface? Radius of earth R= 6400Km.
46. From what height should a piece of ice fall upon the ground so that it is completely
Melted? Assuming all the heat produced remains in ice Latent heat of ice= 80 cal/g,
g= 10m/s²
47. A wave is represented by Y=0.25X10 -3 sin(0.025x - 500t), where y,t and x are in cm
sec and meters respectively. Determine (i) amplitude (ii) period (iii) angular frequency
(iv) wavelength

*****
 VIVEKANANDA P.U COLLEGE PUTTUR
PREPARATORY EXAMINATION
I PUC – PHYSICS
Max Marks: 70
ROLL NO Time: 3:15 hrs

General Instructions:-
1. All parts are compulsory.
2. Part – A questions have to be answered in the first two pages of the answer-booklet.
For Part – A questions, first written-answer will be considered for awarding marks.
3. Answers without relevant diagram / figure / circuit wherever necessary will not carry any marks.
4. Direct answers to the numerical problems without detailed solutions will not carry any marks.

PART A
I. Pick the correct option among the four given options for ALL of the followingquestions:
1. SI unit of luminous intensity is 15x1 = 15
a)lux b)watt c)joule d)candela
2.Slope of position time graph gives
a)velocity b)acceleration c)displacement d)time
3.Magnitude of null vector is
a)unity b)zero c)infinity d)greater than one
4.The trajectory of a projectile thrown from the surface of earth at an angle to the horizontal
a)straight line b)parabola c)circle d)ellipse
5.Impulse is equal to
a)rate of change of momentum b)rate at which energy is transferred
c)work done d)change in momentum
6.Work done by a force is equal to zero if
a)force and displacement are perpendicular
b)force and displacement are parallel
c)force and displacement are antiparallel
d)force and displacement are inclined at 600
7.Angular velocity of each particle of a rotating rigid body about an axis of rotation is
a)same b)different c)depends on relative position d)none
8.Escape speed on a planet does not depend on
a)mass of the planet b)radius of the planet
c)density of the planet d)mass of the object thrown
9.Restoring force developed per unit area is called
a)strain b)modulus of elasticity c)stress d)compressibility
10. Velocity of flow of fluid through a small hole situated at a depth h from the surface of water
filled in a beaker is
a) b) c) √ d) √
11. Which among the following is not the effect of heat?
a)change of state b)change in size c)change in resistance d)change in mass
12. Below are two statements:
(I) In a cyclic process, the total heat absorbed equals the work done by the system
(II) The change in internal energy of the system is zero during cyclic process.
(A)Statement I is wrong but the statement II is correct
(B) Statement I is correct but the statement II is wrong
(C)Both the statements I and II are correct and II is the correct explanation for I
(D)Both the statements I and II are correct and II is not the correct explanation for I
13. The average distance a gas molecule can travel without colliding is called
a)range b)altitude c)mean free path d)stopping distance
14. Angular frequency ω, force constant k and mass of a particle executing SHM are related as

a) ⁄ b) ⁄ c) √ ⁄ d) √ ⁄

15. Sound wave is a

a)mechanical wave b)non-mechanical wave c)transverse wave d)electromagnetic wave

II .Fill in the blanks by choosing appropriate answer given in the brackets for ALL the
following questions: 5x1=5
(Increase,Adiabatic , Zero, Isothermal, Elastic, Decrease )
16. If the distance between the two point masses is increased then the gravitational force
between them will ----------------
17. The surface tension of a liquid decreases with ---------------- in temperature
18. Range for vertically projected particle is ----------------
19. The collision between the gas molecules is ----------------
20. According to Laplace when a longitudinal wave travel in a gas change in pressure and
volume are ------------------

PART B
III. Answer any FIVE of the following questions. 5 x 2 = 10
21. Show that the equation √ ⁄ is dimensionally correct , where the symbols have

the usual meaning.

22. Write x-component and y-component of a vector making an angle Ө with x-axis.
23. Write any two advantages of friction
24. State and explain work-energy theorem for a constant force.
25. Explain the principle of conservation of angular momentum.
26. State and explain Newton’s universal law of gravitation.
27. Define coefficient of volume expansion. Write the expression for it.
28. What is Carnot’s engine ? write the expression for efficiency of Carnot’s engine in terms of
temperatures.
29. What is SHM? Give its graphical representation.

PART C
IV.Answer any FIVE of the following questions. 5 x 3 = 15
30. What is uniform circular motion. Write the expression for centripetal force and explain the
terms.
31. State and explain Newton’s second law of motion. Define S.I unit of force.
32. What is instantaneous power. Derive the expression for power in terms of velocity.
33. A 5kg wheel is given an acceleration of 10rad/s-2 by an applied torque of 2Nm. Calculate its
a)moment of inertia b)radius of gyration
34. Distinguish between ductile and brittle material. Draw stress strain graph for elastic tissue
of aorta.
35. State Pascal’s law. Explain the working of hydraulic lift.
36. Mention the three modes of heat transfer.
37. Write any two features of kinetic theory of gases developed by Maxwell and Boltzmann.
State the law of equipartition of energy
38. Distinguish between the longitudinal and transverse waves
 PART D
V.Answer any THREE of the following questions. 3 x 5 = 15
39. Derive and ⁄ using v-t graph

40. Derive the expressions for maximum height and range of the projectile
41. Give an illustration for conservation of mechanical energy in case of a ball dropped from a
Cliff (freely falling body)
42. a)Define centre of mass. Mention the expression for coordinate of centre of mass of two
particle system. (2)
b)Prove that the time rate of change of the angular momentum of a particle is equal to the
torque acting on it. (3)
43. a)State zeroth law of thermodynamics and what does it signify? (2)
b)Derive the expression for workdone in case of isothermal process (3)
44. what is the phenomenon of beats? Derive the expression for beat frequency.

VI.Answer any TWO of the following questions. 2 x 5 = 10

45. A rubber ball of mass 10g hits the hard surface vertically with a speed 4ms and rebounds
-1

with the same speed. The ball remains in contact with the surface for 0.01sec. Calculate the
average force exerted by the surface.
46. What is the value of acceleration due gravity at a distance 3000km from the centre of the
earth. Given its value on the surface is 9.8ms-2 and the mean radius of the Earth is
6.37X106m.
47. A steel rod of length 0.1m is joined with a copper rod of length 0.05m and the area of cross
section of steel rod is twice that of the copper rod. The free end of the steel rod is in contact
with a furnace at 2000C and free end of copper rod is in contact with ice at 00C. If the
coefficients of thermal conductivity of steel and copper are 50Wm -1K-1 and 385Wm-1K-1,
calculate the temperature of steel-copper junction. Assume that there is no heat loss from
the sides of the rods.
48. A spring having spring constant 1200N/m is mounted on a horizontal table. A mass of 6kg
is attached to the free end of the spring and pulled sideways to a distance of 4cm and
released.
Determine
a) frequency of oscillation b)maximum acceleration c)maximum speed of mass.

***************************

ALL THE BEST

 KEY ANSWER FOR PUC - I YEAR MODEL QUESTION PAPER – 2023-2024
Time: 3 Hrs. 15 Minutes Sub: PHYSICS (33) Max. Marks: 70
General Instructions:
1. All parts are compulsory.
2. For Part – A questions, first written-answer will be considered for awarding marks.
3. Answers without relevant diagram / figure / circuit wherever necessary will not carry any marks.
4. Direct answers to numerical problems without detailed solutions will not carry any marks.
SCHEME OF EVALUATION Date:31-08-2023
Q.No. PART-A Marks
I Pick the correct option among the four given options for ALL of the following questions:
15 X 1 = 15
1. The number of significant figures in 3.500 is .
(A) 2 (B) (C) 4 (D) 1
(C) 4 1
2. A If 𝒗𝑨 𝒗𝑩 and 𝒗𝑪 are the magnitudes of instantaneous velocities
corresponding to the points A, B and C of the given position-time
graph of a particle respectively, then
(A) 𝒗𝑨 = 𝒗𝑩 = 𝒗𝑪 (B) 𝒗𝑨 > 𝒗𝑩 > 𝒗𝑪
(C) 𝒗𝑨 < 𝒗𝑩 < 𝒗𝑪 (D) 𝒗𝑨 < 𝒗𝑩 = 𝒗𝑪

(C) 𝒗𝑨 < 𝒗𝑩 < 𝒗𝑪 1

3. A vector is multiplied with a positive integer. The direction of the resultant vector is
(A) same as the initial vector (B) opposite to the initial vector
(C) perpendicular to the initial vector (D) not specified
(A) same as the initial vector 1
4. ‘An external force is required to keep a body in motion’. This is the statement of
(A) Newton’s first law of motion (B) Newton’s second law of motion
(C) Aristotelian law of motion (D) Newton’s third law of motion
(C) Aristotelian law of motion 1
5. The non-contact force encountered in mechanics is
(A) normal reaction (B) frictional force (C) tension in a spring (D) gravitational force
(D) gravitational force 1
6. 1 calorie is equal to
(A) 𝟒. 𝟏𝟖𝟔 𝑱 (B) 𝟏. 𝟔 𝑿 𝟏𝟎−𝟏𝟗 𝑱 (C) 𝟑. 𝟔 𝑿 𝟏𝟎𝟔 𝑱 (D) 𝟏𝟎 −𝟕 𝑱
(A) 4.186 𝐽 1
7. A girl is sitting with folded hands on a swivel chair rotating with considerable angular
speed. ‘I’ and ‘ω’ are the moment of inertia and angular speed of the chair along with girl
about the axis of rotation. She stretches her arms horizontally while the chair is rotating.
(A) I decreases and ω increases (B) I increases and ω decreases
(C) both I and ω increase (D) both I and ω decrease
(B) I increases and ω decreases 1
8. The SI unit of universal gravitational constant (G) is:
(A) 𝑵 𝒎𝟐 𝒌𝒈−𝟏 (B) 𝑵 𝒎𝟐 𝒌𝒈−𝟐 (C) 𝑵 𝒎 𝒌𝒈−𝟐 (D) 𝑵 𝒎𝟐 𝒌𝒈−𝟑
2 −2
(B) 𝑁 𝑚 𝑘𝑔 1
9. The ratio of lateral strain to longitudinal strain in a stretched wire is called
(A) shear strain (B) compressibility (C) Poisson’s ratio (D) Young’s modulus
(C) Poisson’s ratio 1
10. The angle of contact is acute in case of
(A) water-lotus leaf interface (B) water-waxy surface interface
(C) water-oily surface interface (D) water-glass interface

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 1
 (D) water-glass interface 1
11. The change from solid state to vapour state without passing through the liquid state is
called
(A) vaporisation (B) melting (C) regelation (D) sublimation
(D) sublimation 1
12. Below are two statements:
(I) In a cyclic process, the total heat absorbed equals the work done by the system.
(II) The change in internal energy of the system is zero during cyclic process.
(A) Statement I is wrong but the statement II is correct.
(B) Statement I is correct but the statement II is wrong.
(C) Both the statements I and II are correct and II is the correct explanation for I.
(D) Both the statements I and II are correct and II is not the correct explanation for I.
(C) Both the statements I and II are correct and II is the correct explanation for I. 1
13. The mean free path for gas molecules is given by the expression (with symbols having their
usual meaning)
𝝅 𝟏 𝟏 √𝟐
(A) 𝒍 = (B) 𝒍 = (C) 𝒍 = (D) 𝒍 = 𝝅𝒏𝒅𝟐
√𝟐𝒏𝒅𝟐 √𝟐𝒏𝒅𝟐 √𝟐 𝝅𝒏𝒅𝟐
1
(C) 𝑙 = 1
√2 𝜋𝑛𝑑2
14. The function of time which is not periodic among the following is
(A) 𝒔𝒊𝒏𝝎𝒕 (B) 𝒄𝒐𝒔𝝎𝒕 (C) 𝒆−𝝎𝒕 (D) 𝒔𝒊𝒏𝝎𝒕 + 𝒄𝒐𝒔𝝎𝒕
−𝜔𝑡
(C) 𝑒 1
15. Air column present in an open pipe is vibrating in fundamental mode. It contains
(A) a node and an antinode. (B) a node and two antinodes.
(C) two nodes and an antinode. (D) two nodes and two antinodes.
(B) a node and two antinodes. 1
II Fill in the blanks by choosing appropriate answer given in the brackets for ALL the
following questions: 5 X 1 = 05
(decrease, elastic, elliptical, beats, increase, speed)
16. During uniform circular motion, an object moves in circular path with
constant___________.
speed 1
17. According to Kepler, all planets move in ______________ orbits around the Sun.
elliptical 1
18. The viscosity of liquids decreases with _____________in temperature.
increase 1
19. According to kinetic theory of gases, collisions between the molecules of a gas are
______________.
elastic 1
20. The phenomenon often used by artists to tune their musical instruments is
______________.
beats 1
PART - B
III. Answer any FIVE of the following question: 5 X 2 = 10
21. Mention any two applications of dimensional analysis.
❖ To checking the dimensional correctness (consistency) of equations.
1
❖ Deducing the relation among the physical quantities. 1
❖ To convert unit of one system into unit of another system. (Any Two)

22. Two vectors of same units have magnitude of 8 unit and 5 unit. What are the maximum
and minimum magnitude of resultant that can be obtained with the two vectors?

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 2
 𝐺𝑖𝑣𝑒𝑛: 𝐴 = 8 𝑢𝑛𝑖𝑡 𝑎𝑛𝑑 𝐵 = 5 𝑢𝑛𝑖𝑡 𝑅𝑚𝑎𝑥 = ? 𝑅𝑚𝑖𝑛 = ?
W.K.T. Maximum magnitude of two vector is
𝑅𝑚𝑎𝑥 = 𝐴 + 𝐵
𝑅𝑚𝑎𝑥 = 8 + 5
𝑅𝑚𝑎𝑥 = 13 𝑢𝑛𝑖𝑡 1
W.K.T. Minimum magnitude of two vector is
𝑅𝑚𝑖𝑛 = 𝐴 − 𝐵
𝑅𝑚𝑖𝑛 = 8 − 5
1
𝑅𝑚𝑖𝑛 = 3 𝑢𝑛𝑖𝑡
23. Give any two methods of reducing friction.
Friction can be reduced by
❖ using ball bearings 1
❖ using lubricants like oil, grease etc. 1
❖ polishing the surface.
❖ by streamlining the shape.
❖ using air cushion. (Any Two)
24. State and explain work-energy theorem for a constant force.
Statement: The work done by net force acting on a body is equal to the change in kinetic 1
energy of the body.
If 𝐾𝑖 and 𝐾𝑓 are the initial and final kinetic energies of a body of mass 𝑚 and 𝑊 is the work
done by a constant force then
According to work energy theorem 1
𝐾𝑓 − 𝐾𝑖 = 𝑊
Thus, change in kinetic energy of a body is always equal to work done on the body by the net
force.
25. Mention the two conditions required for the mechanical equilibrium of a rigid body.
The vector sum of the forces acting on the rigid body is zero.
1
𝐹⃗1 + 𝐹⃗2 + ⋯ + 𝐹⃗𝑛 = ∑𝑛𝑖=1 𝐹⃗𝑖 = 0
The vector sum of the torques on the rigid body is zero.
1
𝜏⃗1 + 𝜏⃗2 + ⋯ + 𝜏⃗𝑛 = ∑𝑛𝑖=1 𝜏⃗𝑖 = 0
26. Why does moon has no atmosphere? Explain.
Due to small value of acceleration due to gravity (𝑔) on the surface of the moon, the escape 1
velocity is 2.3 𝑘𝑚𝑠 −1 . Since the air molecules have thermal velocities greater then escape
velocity of moon so the air molecules escape away and cannot form atmosphere on the moon. 1
27. What is meant by thermal expansion? Give relation between coefficient of volume
expansion and coefficient of linear expansion of a material
The phenomenon of change in dimension of a body due to heat supplied is known as thermal 1
expansion.
𝛼𝑣 = 3𝛼𝑙 1
28. What is a Carnot engine? Name the working substance used in it.
An ideal reversible heat engine that operates between source and sink temperatures is known as
Carnot heat engine. 1
Cylinder containing one mole of an ideal gas. 1

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 3
29. Give the positions at which the potential energy of a particle executing SHM will be (i)
maximum and (ii) zero.
1 1
(i) Potential energy is maximum at extreme position. (𝑥 = 𝐴) 𝑈𝑚𝑎𝑥 = 2 𝑚𝜔2 𝐴2
(ii) Potential energy is minimum at mean position. (𝑥 = 0) 𝑈𝑚𝑖𝑛 = 0 1
PART-C
IV. Answer any FIVE of the following questions: 5 x 3 = 15
30. What is meant by range of a projectile? Give the expression for the same. What is the
angle of projection for which the range of a projectile maximum?
The horizontal distance covered by the projectile during its time of flight is called horizontal 1
range of a projectile.
1
𝑣0 2 𝑠𝑖𝑛2𝜃
𝑅=
𝑔
When projectile is projected at an angle 𝜃 = 450 1
31. State and explain Newton’s second law of motion. Define SI unit of force.
Statement: The rate of change of momentum of a body is directly proportional to the applied
force and takes place in the direction of force. 1
Explanation:
If 𝐹⃗ is the force acting on a body of mass 𝑚 and 𝑑𝑝⃗ is change in momentum in time 𝑑𝑡
Then from Newton’s second law,
𝑑𝑝⃗
𝐹⃗ ∝
𝑑𝑡
𝑑𝑝⃗
𝐹⃗ = 𝐾 ( 𝑑𝑡 ) ……. (1)
𝑑𝑝⃗
∵ 𝐾 = 1 and = 𝑚𝑎⃗ Then Eqn. (1) becomes 1
𝑑𝑡
𝐹⃗ = 𝑚𝑎⃗ …… (2)
Definition of S I unit of force:
One newton is that force which acts on a body of mass one 𝑘𝑔 produces an acceleration of one 1
𝑚𝑠 −2.
32. Define work done by a force. Mention two cases in which work done by a force on an
object is zero.
Work is said to be done when applied force causes a displacement. 1
❖ Work done by centripetal force. 1
❖ Work done in pushing an immovable stone. 1
❖ Work done by tension force acting on the string of a simple pendulum. (Any Two)
33. The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16 s.
Calculate the angular acceleration of the wheel assuming the acceleration to be uniform.
𝐺𝑖𝑣𝑒𝑛: 𝜔0 = 1200 𝑟𝑝𝑚 𝜔 = 3120 𝑟𝑝𝑚 𝑡 = 16 𝑠 𝛼 =?
1200 𝑋 2 𝑋 3.14
Initial angular velocity 𝜔0 = 1200 𝑟𝑝𝑚 = = 125.6 𝑟𝑎𝑑𝑠 −1
60
3120 𝑋 2 𝑋 3.14 1
Final angular velocity 𝜔 = 3120 𝑟𝑝𝑚 = = 326.6 𝑟𝑎𝑑𝑠 −1
60
W.K.T. Angular acceleration in case of rotational motion is
𝜔 − 𝜔0 326.6 − 125.6 1
𝛼= =
𝑡 16
𝛼 = 12.56 𝑟𝑎𝑑𝑠 −2 1
34. Distinguish between the three different moduli of elasticity of a material.

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 4
 1) Young’s modulus: (Y) With in elastic limit, the ratio of longitudinal stress to longitudinal 1
strain is called Young’s modulus.
2) Shear Modulus or rigidity modulus: (G) With in elastic limit, the ratio of shearing stress to
1
the corresponding shearing strain is called shear modulus.
3) Bulk Modulus: (B) With in elastic limit, bulk modulus is the ratio of volume stress to volume 1
strain.
35. State Bernoulli’s principle. Give Bernoulli’s equation in fluid dynamics. What is Magnus
effect?
Statement: For an incompressible, non-viscous fluid in streamline flow, the sum of pressure
energy, kinetic energy and potential energy per unit volume at any part remains constant. 1
Bernoulli’s equation:
1 1
𝑃 + ( ) 𝜌𝑣 2 + 𝜌𝑔ℎ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
2
Magnus effect: The difference in lateral pressure, which causes a spinning ball to take a curved 1
path which is curved towards the greater pressure side is called magnus effect.
36. Explain briefly the land breeze.
During night, the land cools faster than sea water. 1
Due to this water surface is warmer at night than the land. 1
As a result, air from the land (high pressure region) moves towards the sea (low pressure
region). This is called land breeze. 1
37. Using the expression of total internal energy of one mole of monatomic gas, obtain the
expression for the molar specific heat of a monatomic gas at constant volume.
W.K.T.
According to law of equipartition of energy, the average energy associated with 3 degree of
1 3
freedom per molecule is 〈𝐸〉 = 3 (2 𝐾𝐵 𝑇) = (2) 𝐾𝐵 𝑇 1
3
∴ Total internal energy of one mole of a monoatomic gas is 𝑈 = (2 𝐾𝐵 𝑇) 𝑋 𝑁𝐴 ……. (1)

But, 𝐾𝐵 𝑋 𝑁𝐴 = 𝑅 Universal gas constant

3
∴ 𝑈 = 2 𝑅𝑇 ……… (2)
1
𝑑𝑈
W.K.T. The molar specific heat at constant volume is 𝐶𝑉 = 𝑑𝑇

𝑑 3
𝐶𝑉 = ( 𝑅𝑇 )
𝑑𝑇 2
3 1
𝐶𝑉 = 2 𝑅 …… (3)

38. Define (i) frequency and (ii) wavelength of a wave. Give an example for non-mechanical
wave.
(i) Frequency: The number of waves set up in a medium in one second is called wave 1
frequency.
(ii) Wavelength: Wavelength of a wave is the distance between any two constructive crests or
1
troughs of a transverse wave.
Example: Light waves, Radio waves, 𝑋-rays, 𝛾 −rays etc. (Any One) 1
PART-D
V Answer any THREE of the following questions: 3 x 5 = 15

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 5
39. 𝟏
Derive the equation 𝒙 = 𝒗𝟎 𝒕 + 𝟐 𝒂𝒕𝟐 using v-t graph.
Velocity time graph is graph obtained by plotting velocity of a body along 𝑦 − 𝑎𝑥𝑖𝑠 and time
along 𝑥 − 𝑎𝑥𝑖𝑠.
Consider a body moving with initial velocity 𝑣𝑜 and later
subjected to uniform acceleration 𝑎 as shown in 𝑣 − 𝑡 graph.

𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 →
W.K. T 1
Area under 𝑣 – 𝑡 graph gives displacement of a body.

∴ 𝑥 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑟𝑎𝑝𝑒𝑧𝑖𝑢𝑚 𝑂𝐴𝐵𝐷 1

Or 𝑥 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 𝑂𝐴𝐶𝐷 + 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑟𝑎𝑖𝑛𝑔𝑙𝑒 𝐴𝐵𝐶

1 1
𝑥 = 𝑂𝐴 𝑋 𝐴𝐶 + 2 𝑋 𝐴𝐶 𝑋 𝐵𝐶 ….. (1)

From fig. 𝑂𝐴 = 𝑣𝑜 𝐴𝐶 = 𝑡 𝑎𝑛𝑑 𝐵𝐶 = (𝑣 − 𝑣0 ) = 𝑎𝑡

1
Then eqn. (1) becomes
1
𝑥 = 𝑣𝑜 𝑡 + 𝑡 𝑋 𝑎𝑡
2
1
𝑂𝑟 𝑥 = 𝑣𝑜 𝑡 + 2 𝑎𝑡 2 ……….. (2) 1
40. Show that the trajectory of a projectile is a parabola.
Consider a projectile which is
projected with an initial
velocity 𝒗𝟎 at an angle 𝜃 as 𝑣0 𝑐𝑜𝑠𝜃 1
𝑣0
shown in figure.
Let 𝑥 be the horizontal
distance travelled by the
projectile in time 𝑡 than 1
𝑥 = (𝑣0 𝑐𝑜𝑠𝜃) 𝑋 𝑡
𝑥
𝑡=𝑣 ……….. (1)
0 𝑐𝑜𝑠𝜃

Let 𝑦 be the vertical distance travelled by the projectile in same time 𝑡 then
1
𝑦 = (𝑣0 𝑠𝑖𝑛𝜃) 𝑋 𝑡 + (−𝑔) 𝑋 𝑡 2
2
Or
1
𝑦 = (𝑣0 𝑠𝑖𝑛𝜃) 𝑡 − 𝑔𝑡 2 ………. (2) 1
2
Put Eqn. (1) in Eqn. (2)
𝑥 1 𝑥 2
𝑦 = (𝑣0 𝑠𝑖𝑛𝜃) ( )− 𝑔( )
𝑣0 𝑐𝑜𝑠𝜃 2 𝑣0 𝑐𝑜𝑠𝜃
𝑔
𝑦 = 𝑥 𝑡𝑎𝑛𝜃 − (2 𝑣 2 𝑐𝑜𝑠2 𝜃
) 𝑥 2 ……… (3)
0

This equation is in the form of 𝑦 = 𝑎𝑥 − 𝑏𝑥 2 ……….. (4) 1

𝑔
Eqn. (4) represents an equation of parabola with 𝑎 = 𝑡𝑎𝑛𝜃 and 𝑏 = (2 𝑣 2 𝑐𝑜𝑠 2 𝜃
)
0

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 6
 Thus, the trajectory of a projectile is parabola. 1
41. Obtain the expressions for final velocities of two particles undergoing completely elastic
collision in one-dimension considering second body to be initially at rest.
Consider a body of mass 𝑚1 moving initially with velocities 𝑢1 collide elastically with a body
of mass 𝑚2 which is at rest (𝑢2 = 0) and move with final velocities 𝑣1 and 𝑣2 in same
direction as shown in fig.
Since collision is elastic both momentum and kinetic energy are conserved.

From law of conservation of momentum

𝑚1 𝑢1 + 0 = 𝑚1 𝑣1 + 𝑚2 𝑣2 …….. (1)
Or 𝑚1 (𝑢1 − 𝑣1 ) = 𝑚2 𝑣2 ………. (2) 1

From law of conservation of energy

1 1 1
𝑚1 𝑢12 + 0 = 𝑚1 𝑣12 + 𝑚2 𝑣22
2 2 2
1
Or 𝑚1 (𝑢12 − 𝑣12 ) = 𝑚2 𝑣22 …….. (3)
Divide Eqn. (3) By Eqn. (2)
𝑚1 (𝑢12 − 𝑣12 ) 𝑚2 𝑣22
=
𝑚1 (𝑢1 − 𝑣1 ) 𝑚2 𝑣2
(𝑢1 + 𝑣1 )(𝑢1 − 𝑣1 )
= 𝑣2 1
(𝑢1 − 𝑣1 )
Or 𝑣2 = 𝑢1 + 𝑣1 …… (4)
Put Eqn. (4) in Eqn. (1)
𝑚1 𝑢1 = 𝑚1 𝑣1 + 𝑚2 (𝑢1 + 𝑣1 )
𝑚1 𝑢1 = 𝑚1 𝑣1 + 𝑚2 𝑢1 + 𝑚2 𝑣1
𝑚1 𝑢1 − 𝑚2 𝑢1 = 𝑚1 𝑣1 + 𝑚2 𝑣1
( 𝑚1 − 𝑚2 )𝑢1 = ( 𝑚1 + 𝑚2 )𝑣1
𝑚 −𝑚 1
Or 𝑣1 = ( 𝑚1 +𝑚2 ) 𝑢1 …… (5)
1 2

2𝑚1
Similarly, 𝑣2 = ( 𝑚 ) 𝑢1 …… (6) 1
1 +𝑚2

42. a) What is a rigid body? What type of motion is observed in a rigid body which is pivoted
at the centre of mass? (2)
b) Prove that the time rate of change of the angular momentum of a particle is equal to the
torque acting on it. (3)

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 7
 a) A rigid body is one in which the distance between all pairs of particles do not change during the 1
motion of the body.
Rotational motion 1

b) W.K.T angular momentum of a particle having linear momentum 𝑃⃗⃗ and position vector 𝑟⃗ is
given by
𝑙⃗ = 𝑟⃗ 𝑋 𝑝⃗ ……… (1)
Differentiate Eqn. (1) with respect to time 1
𝑑 𝑙⃗ 𝑑
i.e., = 𝑑𝑡 (𝑟⃗ 𝑋 𝑝⃗)
𝑑𝑡

On differentiating we get
𝑑 𝑙⃗ 𝑑𝑟⃗ 𝑑 𝑝⃗
= 𝑋 𝑝⃗ + 𝑟⃗⃗⃗ 𝑋 …... (2)
𝑑𝑡 𝑑𝑡 𝑑𝑡
𝑑𝑟⃗
Since 𝑑𝑡 = 𝑣⃗ and 𝑝⃗ = 𝑚𝑣⃗ then Eqn. (2) becomes
1
𝑑 𝑙⃗ 𝑑 𝑝⃗
= 𝑣⃗ 𝑋 𝑚 𝑣⃗ + 𝑟⃗⃗⃗ 𝑋 Since 𝑣⃗ 𝑋 𝑣⃗ = 0
𝑑𝑡 𝑑𝑡

𝑑 𝑙⃗ 𝑑 𝑝⃗
∴ = 𝑟⃗⃗⃗ 𝑋 …… (3)
𝑑𝑡 𝑑𝑡
𝑑 𝑃⃗⃗
Since = 𝐹⃗ Rate of change of linear momentum represents force.
𝑑𝑡

𝑑 𝑙⃗
Then = 𝑟⃗⃗⃗ 𝑋 𝐹⃗ = 𝜏⃗
𝑑𝑡

𝑑 𝑙⃗
∴ = 𝜏⃗ ……… (4) 1
𝑑𝑡
Thus, rate of change of angular momentum of a particle is equal to the torque acting on it.
43. a) State and explain first law of thermodynamics. (2)
b) Mention any three differences between isothermal and adiabatic processes. (3)
a) Statement: The quantity of heat which is capable of doing work absorbed by the system will be
1
equal the sum of the increase in its internal energy and the work done by the system on the
surroundings.
Explanation: If ∆𝑄 is the amount of heat supplied to the system by the surrounding, ∆𝑊 is the
work done by the system on the surrounding and ∆𝑈 is change in internal energy of the system
then
According to first law of thermodynamics, ∆𝑄 = ∆𝑈 + ∆𝑊 1
b) Isothermal Process Adiabatic Process
• In isothermal process temperature of the • In adiabatic process there is no exchange
system remain constant. of heat between the system and the 1
surrounding.
• Equation of state is 𝑃𝑉 = Constant. • Equation of state is 𝑃𝑉 𝛾 = Constant. 1
• It is a slow process. • It is a fast process. (Any Three)
• Pressure is more at a given volume. • Pressure is less at a given volume. 1
Example: Freezing of water, Melting of ice • Example: Bursting of tyre, rapid
etc. compression, Filling of air to a bicycle
tube etc.

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 8
44. Write Newton’s formula for speed of sound in air. Explain why and how Laplace modified
Newton’s formula for speed of sound.
Newton’s formula of velocity of sound in air
𝑃
𝑣 = √𝜌 1
Explanation: According to Laplace, changes in pressure during the propagation of sound wave
through a gas take place under adiabatic conditions because air is bad conductor of heat and
changes are very rapid and there is no time for equalization of temperature.
For adiabatic process, 1
𝑃𝑉 𝛾 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ….. (1)
Differentiating on both sides with respect to V we get
𝑑(𝑃𝑉 𝛾 ) 𝑑𝑃 1
= 0 => 𝑃𝛾𝑉 𝛾−1 + 𝑉 𝛾 =0
𝑑𝑉 𝑑𝑉

𝑃𝛾𝑉 𝛾−1 𝑑𝑉 + 𝑉 𝛾 𝑑𝑃 = 0

Or 𝑃𝛾𝑉 𝛾−1 𝑑𝑉 = −𝑉 𝛾 𝑑𝑃

𝑉 𝛾 𝑑𝑃 𝑉𝑑𝑃
𝛾𝑃 = − 𝛾−1 =−
𝑉 𝑑𝑉 𝑑𝑉

𝑑𝑃
𝛾𝑃 = − 𝑑𝑉 = 𝐵𝑢𝑙𝑘 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 (𝐵) ……….. (2) 1
( )
𝑉
Hence under adiabatic process 𝐵 = 𝛾𝑃
∴Newton-Laplace formula for velocity of sound in air is
𝛾𝑃
𝑣 = √𝜌
At STP and for air

𝛾𝑃 1.41 𝑋 1.013 𝑋 105

𝑣 = √𝜌 = √ = 332 𝑚𝑠 −1
1.293
1
This value agrees with the experimental value.
I. Answer any TWO of the following questions: 2 x 5 = 10
45. A body of mass of 8 kg is suspended by a rope of length 2.5 m from the ceiling. A force of
60 N is applied on the body in the horizontal direction. Find the angle that the rope makes
with the vertical in equilibrium. (Take 𝒈 = 𝟏𝟎 𝒎𝒔−𝟐 ). Neglect the mass of the rope.
𝐺𝑖𝑣𝑒𝑛: 𝑚 = 8 𝑘𝑔 𝑙 = 2.5 𝑚 𝐹 = 60 𝑁 𝑔 = 10 𝑚𝑠 −2 𝜃 = ?

𝑇2
𝜃
𝑇1
𝜃 1
𝑇1 𝑇1 𝑐𝑜𝑠𝜃
𝑃 60 𝑁
𝑇2 𝑊 𝑇1 𝑠𝑖𝑛𝜃 60 𝑁
𝑃

𝑇2
80 𝑁 80 𝑁

From free body diagram of W

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 9
 𝑇2 = 𝑚𝑔
1
𝑇2 = 8 𝑋 10 = 80 𝑁
From Free body diagram of P
𝑇1 𝑐𝑜𝑠𝜃 = 𝑇2 = 80 𝑁 …. (1) 1
𝑇1 𝑠𝑖𝑛𝜃 = 𝐹 = 60 𝑁 …… (2)
From Eqn. (1) and Eqn. (2)
6 1
𝑡𝑎𝑛𝜃 = = 0.7500
8
𝜃 = 𝑡𝑎𝑛−1 (0.7500)
𝜃 = 36.870 1

46. Assuming the earth to be a sphere of uniform mass density, how much would a body weigh
at a depth equal to half the radius of the earth if it weighs 250 N on the surface of earth?
What will the weight of the same body at the centre of the earth?
𝑅
𝐺𝑖𝑣𝑒𝑛: 𝑊 = mg = 250 N 𝑑 = 2 𝑊𝑑 = ? 𝑊𝐶 = ?

W.K T. Acceleration due to gravity at a depth below the earth’s surface is

𝑑
𝑔′ = 𝑔 (1 − ) 1
𝑅
𝑅
∵ 𝑑=
2
𝑅⁄ 1
2
𝑔′ = 𝑔 (1 − ) = 𝑔 (2)
𝑅
1
′
𝑔
𝑔 =
2
∴ New weight 𝑊𝑑 = 𝑚𝑔′
𝑚𝑔
𝑊𝑑 = 1
2
250
𝑊𝑑 = = 125
2 1
𝑊𝑑 = 125 𝑁
Weight of a body at the centre of the earth is zero ∴ 𝑔 = 0
1
𝑊𝐶 = 0
47. A copper plate of mass 2 kg is heated to a temperature of 𝟔𝟎𝟎𝟎 𝑪 and then placed on large
ice block at 𝟎𝟎 𝑪. Calculate (i) the maximum quantity of heat that the copper plate can
transfer to ice block and ii) the maximum amount of ice it can melt. Given: Specific heat of
capacity of copper = 𝟑𝟗𝟎 𝑱 𝒌𝒈−𝟏 𝑲−𝟏 and latent heat fusion of water = 𝟑𝟑𝟑 × 𝟏𝟎𝟑 𝑱 𝒌𝒈−𝟏 .
𝐺𝑖𝑣𝑒𝑛: 𝑚𝐶 = 2 𝑘𝑔 𝜃1 = 6000 𝐶 𝜃2 = 00 𝐶 ∆𝑇 = (𝜃1 − 𝜃2 ) = 6000 𝐶 𝑆𝐶 = 390 𝐽 𝑘𝑔−1 𝐾 −1
3 −1
𝐿𝑊 = 333 𝑋 10 𝐽 𝑘𝑔 𝑄𝑖 =? 𝑚𝑖 =?
W.K.T. Heat lost by copper plate 𝑄𝐶 = 𝑚𝐶 𝑋 𝑆𝐶 𝑋 ∆𝑇 1
3
𝑄𝐶 = 2 𝑋 390 𝑋 600 = 468 𝑋 10 𝐽

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 10
 From principle of calorimetry
Heat lost by copper = heat gained by ice.
1
𝑖. 𝑒. , 𝑄𝐶 = 𝑄𝑖
3
𝑄𝑖 = 468 𝑋 10 𝐽 1
Let 𝑚𝑖 be mass of ice melted then
𝑄𝑖
𝑚𝑖 =
𝐿𝑊 1
3
468 𝑋 10
𝑚𝑖 =
333 𝑋 103
𝑚𝑖 = 1.405 𝑘𝑔 1
−𝟏
48. A block of mass 1 kg is fastened to a spring. The spring has a spring constant of 𝟓𝟎 𝑵𝒎 .
The block is pulled to a distance x = 10 cm from its equilibrium position at x = 0 on a
frictionless surface from rest at t = 0 and is released. Calculate (i) angular frequency of
oscillations of the block and (ii) the maximum speed with which the block crosses the mean
position.
𝐺𝑖𝑣𝑒𝑛: 𝑚 = 1 𝑘𝑔 𝐾 = 50 𝑁𝑚−1 𝐴 = 10 𝑐𝑚 = 0.1 𝑚 𝜔 = ? 𝑣𝑚𝑎𝑥 =?
W.K. T.
(i) Angular frequency of oscillation of a spring is
1
𝐾
𝜔 = √𝑚

50
𝜔 = √1 1
𝜔 = 7.07 𝑟𝑎𝑑 −1
1
(ii) The maximum velocity of the spring is
1
𝑣𝑚𝑎𝑥 = 𝜔𝐴
𝑣𝑚𝑎𝑥 = 0.1 𝑋 7.07
1
𝑣𝑚𝑎𝑥 = 0.707 𝑚𝑠 −1
Note: Any other alternate correct method /answer should be considered

*******

Prof: Venugopal H. R. MSc, MPhil, B.Ed; Lecturer in Physics K.L.E. P C Jabin PU College of Science, Hubballi Ph:9886739600 Page 11