National Standard Examination In Physics -1999-(1)

1. The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also
doubled. The angle between the tow forces is
(A) 120 (B) 60
(C) 180 (D) 90

1. A.
R = (3P) + (2P) + 2 (3P  2P)cos 
2 2 2

(2R) = (6P) + (2P) + 2 (6P  2P) cos 

2 2 2

Solving : cos  = 1/2

 = 120

2. To a man walking at the rate of 4 kmph, the rain appears to fall vertically. If the apparent velocity
of rains is 43 kmph. Then inclination of the real velocity of the rain with the vertical will be
(A) 60 (B) 30
(C) 45 (D) 90

2. B.
Apparent vel of rain = vel of rain  vel of man
1
tan  
3
 = 30

3. If the earth were to stop rotating, the value of ‘’g ‘’ the acceleration due to gravity, at Delhi.
(A) increases (B) decreases
(C) unchanged (D) becomes zero

3. A.
Centrifugal force will be absent ‘g’ will increase

4. A particle of mass m at rest in acted upon by a force P for time t. Its kinetic energy after time t is
P2 t 2 P2 t 2
(A) (B)
m 2m
2 2
Pt P2 t 2
(C) (D)
3m 2m

4. B.
P Pt
a , v = at =
m m
2
1 1  Pt  P2 t 2
KE  mv 2 = m  
2 2  m  2m

5. Two forces (P + Q) and (P  Q) a point have their resultant 2(P2  Q2 ) . Then the angle between
them must be
(A) 90 (B) 180
(C) 0 (D) 45
5. A.
[ 2(P2  Q2 )]2  (P  Q)2  2(P  Q)(P  Q)cos 
2(P + Q ) = 2 (P + Q ) + 2(P  Q ) cos 
2 2 2 2 2 2

 2(P  Q ) cos  = 0
2 2

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 National Standard Examination In Physics -1999-(2)

cos  = 0
  = 90

6. A simple pendulum of length L has period T on earth and Ts in a satellite. Then

(A) T > Ts (B) T < Ts
(C) T = Ts (D) Ts cannot be measured.

6. D.
In a satellite all bodies are in a state of weightlessness
g=0
 T can not be measured

7. The mass and the diameter of planet are twice that of earth. The seconds pendulum on earth will
have its period on this planet equal to
(A) 2 sec (B) 22 sec
(C) 1 sec (D) 42 sec

7. B.
1
On earth  T = 2
g
1
On planet  t '  2
g

T' g GM / R 2
 
T g' G2m /(2R)2
2
=
1
t = 2 t = 22 SEC

8. A solid sphere of radius R and a hollow sphere of inner radius r and outer radius R made of
copper are heated to the same temperature and are allowed to cool in the same environment.
Then,
(A) Hollow sphere cools faster
(B) Solid sphere cools faster
(C) Both the spheres attain room temperature at the same time.
(D) The rate of loss of heat of the solid sphere is twice that of the hollow sphere.

8. A.
Rate of loss of heat
d
 mass  sp. ht  is same
dt
d
Since mass of hollow sphere is less its is more
dt
 Hollow sphe. Cools faster

9. Two identical glass spheres filled with air are connected by a horizontal glass tube. The glass
tube contains a pellet of mercury at its mid point. Air in one sphere is at 0C and the other is at
20C. If both the vessels are heated through 10C then neglecting the expansions of the bulbs
and the tube.
(A) The mercury pellet gets displaced towards the sphere at lower temperature.
(B) The mercury pellet gets displaced towards the sphere at higher temperature.
(C) The mercury pellet does not get displaced at all.
(D) The temperature rise causes the pellet to expand without any displacement.

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 National Standard Examination In Physics -1999-(3)

9. B.
Let the initial pressure of the spheres be ” when heated let the pressures be 1 and 2 of the
spheres having initial temperatures 0C and 20C respectively then.
1 283
  1.037
 273
 303
and 2   1.034
 293
1  2
thus the mercury pellet will be displaced to words the sphere at higher temp.

10. Three rods of same material form an isosceles triangle (the two angles at the base are equal.)
When the structure is heated the base angles of the triangle will.
(A) increase (B) not change
(C) decrease (D) be doubled

10. B. A
MC
cos  
AC
After heating B 
C
MC(1   ) M
cos  
AC(1  t)
  remains same.

11. A concave mirror, forms a real image of an object. If the whole arrangement is immersed in water.
Then the image will.
(A) Disappear (B) shift towards the mirror
(C) Shift away from the mirror (D) Now suffer any change in its position.

11. D.
Reflections are not affected by medium

12. One surface of a lens is convex and other is concave. If the radii of curvature are r1 and r2
respectively, the lens will be convex, if
(A) r1 > r2 (B) r1 = r2
(C) r1 < r2 (B) r1 = 1/r2

12. C
1 1 1
 (  1)   
f  r1 r2 
1 1
   must be +Ve
 r1 r2 
1 1
 
r1 r2
r1 < r2

13. When a small lamp is half 1.5 m above the surface of water in a tank, its image formed by
reflection at the surface appears to coincide with the image of the bottom of the tank. ( of water =
4/3). The depth of the tank is
(A) 2 m (B) 1.5 m
(C) 1 m (D) 4 m

13. A.

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 National Standard Examination In Physics -1999-(4)

Real depth 4
 , App depth = 1.5 m
App depth 3
 Real depth = 2m

14. A ray of light is incident at angle of 60 on a face of prism of angle 30. The emergent ray makes
and angle of 30, with the incident ray. The emergent ray will
(A) graze the surface from which it emerges.
(B) Be normal to the surface from which it emerges.
(C) Make an angle of 60 with the surface from which it emerges.
(D) Emerges from the same surface

14. B.
A +  = I + e (e = angle of emergence)
30 + 30 = 60 + e
e=0

15. A sound wave travels from air to water. The angle of incidence is 1 and the angle of refraction is
2 Assuming Snell’s law to be valid.
(A) 2 < 1 (B) 2 > 1
(C) 2 = 1 (D) 2 = 90

15. B.
Sound travels faster in water
2 is greater 2 > 1

16. A vertical pillar of soft iron partially embedded in earth in the Northern Hemisphere is found to be
magnetized by the earth’s magnetic field. The polarity at the top end of the pillar will be
(A) South pole
(B) North pole
(C) Will change from South to North according to the time of the day
(D) None of these

16. A.
The pillar is magnetised by induction. In the phenomenon of induction the near end is oppositely
magnetised and fat end is similarly magnetised. In the north hemisphere of earth it is the “South”
pole of earth’s magnet
 The top end of the pillar is “South pole”.

17. Two resistances 300 ohm and 400 ohm are connected in series with a 60 volt supply. A voltmeter
connected across 400 ohm reads 30V. The same voltmeter when connected across the other
resistance will read.
(A) 22.5 V (B) 50 V
(C) 30 V (d) 10 V

17. A.
300  300 
voltmeter across 400  in the figure a. V
1 1 1 60 V
  
300 400 G 400 
V
 G = 1200  (Res of voltmeter) 50 V
now across 300  in figure b.
1 1 1
 
r 300 1200
 r = 240 

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 National Standard Examination In Physics -1999-(5)

Exr
 V  22.5 V
r  400

18. The energy of an electron in excited Hydrogen atom is 3.4 eV. Then according to Bohr’s Theory
the angular momentum of this electron in Js is
(A) 2.11  1034 (B) 3  1034
34
(C) 2  10 (D) 0.5  1034

18. A.
1
En = 3.4 eV En 
n2
 E1  13.6 eV
n=2
nh 2h h
Angular momentum =    2.11 10 34 Js
2 2 

19. A parallel plate capacitor has charge Q coal, potential V volt. And energy E joule. A dielectric slab
is now inserted between the two plates, then
(A) V and E both decrease, (B) V and E both increase,
(C) V decreases, E increases (D) V increases, E decreases

19. A.
On introducing the dielectric slab. C increases. Q remains constant hence V decreases (Q=VC).
2
And E also decreases (E = Q /2C).

20. For rectilinear motion quantities represented in the following graph are y
(A) (v, u) (B) (s, t)
(C) (v, a) (D) (a, t)
x

20. B.
The graph shown in a case of body thrown up vertically

21. A bird flies with a speed of 10 kmph and a car moves with uniform speed of 8 kmph. Both start
from B towards A (BA = 40 km), at the same instant. The bird having reached A, flies back
immediately to meet the approaching car. As soon as it reaches the car it flies back to A. Thus the
bird repeats till both the car and the bird simultaneously. The total distance flown by the bird is
(A) 80 km (B) 40 km
(C) 50 km (D) cannot be determined.

21. C.
Car takes 5 hours to reach A
In this 5 hours bird will fly 5  10 = 50 km

22. With reference to the figure, showing a light inextensible string passing
over a fixed frictionless pulley, the tension T3 is
(A) 24.5 N (B) 29.4 N
(C) 18.6 N (D) 68.6 N
T1 T2
22. A.
Masses 4 & 3 kg move down and 5 kg moves up 5 kg 4 kg
75 9 T3
a g  . Consider motion of 3 kg mass
75 8
2 kg
3g
Mg  T3  Ma  Ta = 3g  = 2.5g = 24.5 N
6
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 National Standard Examination In Physics -1999-(6)

23. For a system of particles the following two statements are possible:
(1) K.E. of system is zero &
(2) The linear Momentum of the system is zero than.
(A) (1) implies (2) and (2) implies (1) (B) neither (1) implies (2), nor (2) implies (1)
(C) (1) implies (2) but (2) does not imply (2) (D) (2) implies (1) but (1) does not imply (2)

23. C.
Linear momentum = 0 does not imply KE = 0 but if KE = 0. Then momentum = 0.

24. A tube one metre long is filled with liquid of mass 1 kg. The tube is closed at both the ends and is
revolved about one end in a horizontal plane at 2 rev/Sec. The force experienced by the lid at the
other end is
2 2
(A) 4 N (B) 8 N
2 2
(C) 16 N (D) 9.8 N

24. B.
2
Force = m r
2
= 1(22)
2
= 8 N

25. The surface tension phenomenon is the result of the tendency of a system to
(A) Conserve energy (B) Keep p.e. minimum
(C) Conserve volume (D) Keep surface area minimum

25. B

26. A balloon filled with Hydrogen rises in air. A submarine loaded with ballast sinks in the ocean.
Assuming that the mass of the Hydrogen in balloon and the ballast in the submarine is constant.
(A) Balloon will keep on ascending while submarine keeps descending.
(B) Balloon will keep on ascending while submarine will reach a certain depth and halt.
(C) Balloon will reach certain height and halt while submarine keeps descending
(D) Both will reach certain height/depth an halt.

26. C.
A balloon filled with H2 will rise to a certain height when equilibrium is reached up trust = mg. The
force on submarine is mg-uptrust and the uptrust remains same as density of water is constant
(liquids are in compressibles)

27. A water tank of height 10m. completely filled with water is placed on a level ground. It has two
holes on at 3m and the other at 7m from its base. The water ejecting from.
(A) Both the holes will fall at the same spot
(B) Upper hole will fall farther than that from the lower hole.
(C) Upper hole will fall closer than that from the lower hole
(D) More information is required.

27. A.
Velocity of out coming water from hole A = V1 = 2gh
Hole B = V2  2g(He  h)
2(H0  h)
Time of reaching the ground from hole A  t1 
g
2h
Hole B = t 2 
g
Obviously range on the ground for both is the same R = V1t1 =V2t2
 2g h(H0  h)
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 National Standard Examination In Physics -1999-(7)

A metal rod having cross section area 1.00 cm; length 20.0 cm, Y = 1.05  10 N/m ,  = 1.0 
11 2
28.
106/C is supplied 40 calories of heat, the energy stored in the rod is
(A) 4.2 J (B) 420 J
(C) 144 J (D) 168 J

28. D.
Energy stored = 40 cal
= 168 J

29. In case of liquid when anamolous expansion occurs

(A) Temperature, volume increase, density increases.
(B) Volume, density increase temperature decreases
(C) Volume, temperature decrease, density decreases
(D) Density, temperature decrease, volume increases.
29. D.
Density temperature decrease, vol. increases
30. Red shift is an illustration of
(A) Low temperature emission (B) High frequency absorption
(C) Doppler effect (D) Unknown phenomenon
30. C.
Doppler effect
31. Speed of light is very large but finite. If it were to be infinite then
(A) Sun will rise earlier (B) Sun will set later
(C) Duration of the body will be shortened (D) Unknown phenomenon
31. D
32. Red, Green and Blue are Primary colours. Yellow is complementary colour of Blue. Then the
incorrect statement is
(A) Red + Green  Yellow (B) Red + Green + Blue  White
(C) Yellow + Blue  White (D) Red + Blue  Violet
32. D.
d is subtractive phenomenon a, b, c are additive
A body radiates 2.7  10 J/s at 127C. It will radiate 4.32  10 J/s when its temperature is
3 8
33.
(A) 2527C (B) 7727C
(C) 2540C (D) 2773C
33. B.
2.7  103 4004
 (Stefan’s Law)
4.32  108 T4
T = 400  20 = 8000 K
= 7727C
34. A rod works as a heater that consumes one kW of power. If it is cur along the length at two
mutually perpendicular diameters to form 4 rods, the wattage of each new rod will be.
(A) 1 Kw (B) 0.25 Kw.
(C) 4 Kw (D) 16 Kw

34. B.
V2
Area decreases by ¼ R increases 4 times. Power =  0.25 KW
R

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 National Standard Examination In Physics -1999-(8)

35. The current in the branch AB is

1 1
(A) 1 A (B) 2 A 2
(C) 1.5 A (D) 3 A
6V I

4
2 2

35. B.
1 2
6V
Current  2A
3 2 4 1 2
1 2

36. When heavy water is electrolysed, the ratio of mass of deuterium to Oxygen liberated is
(A) 1 : 17 (B) 1 : 32
(C) 1 : 8 (D) 1 : 4
36. D.
Heavy water id D2O
Mass of Heavy Hydrogen (deutirium) (D) = 2
Mass of Oxygen = 16
D2  4
 D2; O = 4 : 16
O = 16 = 1: 4

37. The forward biased diode is +2V 2V

(A) A (B) B
(C) C (D) D 2V +2V

37. A. 4V 3V

All others have cathode at higher potential than anode
2V 2V

38. A wire of length L is bent to form a circle and a current I is passed through it. Now the same wire
is bent into a coil of two turns and the same current is passed through is, the magnetic induction
at the centre now as compared to its value in the first case is
(A) One quarter (B) One half
(C) Twice (D) four times
38. D.
0 11  21
B1  and B2  0
4r1 2r2
B1 r 4 / 2.2 1
 2  
B2 2r1 2.4 / 2.1 4
 B1 = 4B1

39. The magnetic induction associated with current flowing in a hollow copper tube will be
(A) Only inside (B) Only outside
(C) Both outside and inside (D) Neither inside nor outside
39. B.
Only outside
40. A longitudinal wave is represented by
 x
x  x 0 Sin 2  nt  
 
The maximum particle velocity will be four times the wave velocity if
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 National Standard Examination In Physics -1999-(9)

 0
(A)   (B)   2x0
4
 0
(C)   (D)   4x 0
2
40. C.
dx  x
Particle vel =  x 0 2n cos 2  nt  
dt  

max particle vel = x02n putting cos term = 1 wave vel =  n
T
for x02n = 4n
x0 
 
2

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 National Standard Examination In Physics -1999-(10)

SUB PART A-2

41. The part of Physical quantities having same dimensions is

(A) Angular momentum and Planck’s constant
(B) Impulse and momentum
(C) Moment of inertia and moment of a force
(D) Young’s Modulus and stress

41. A, B, D

42. A body suspended from a fixed support by a rubber band executes oscillations in a vertical plane.
Its period is
(A) Independent of its mass (B) Dependant on “g”
(C) Smaller for a thicker band (D) Independent of initial displacement

42. C, D

43. A1 and B1 are two bubbles joined by a thin tube, similarly A2 and B2 are Soap Bubbles
rubber balloons filled with air joined by another thin tube (Fig shows the
situation) As time progress _____choose the correct statement. B1 A1
(A) A1 will shrink : B2 will shrink (B) A1 will shrink : A2 will expand Gas Bubbles
(C) A1 will expand : B2 will shrink (D) A1 will expand : B2 will expand
B2 A2

43. C, D

44. A source of light is at distance “S” from metal plate. The plate emits electrons having stopping
potential “V”. Then the wrong statement are
(A) V decreases as s increase
(B) V decreases as s decreases
(C) V increases when frequency of light is increased
(D) V alters if metal is changed.

44. A, B

45. In case of transistor, collector collects maximum number of electron injected by the emitter in the
base region, because
(A) Collector base junction is of larger area (B) Base width is small
(C) Emitter base diode is reverse biased (D) None of the above

45. A, B

46. In case of radioactive radiations

(A) Some are not deviated by electric magnetic fields
(B) Some carry negative charge
(C) All are electromagnetic waves
(D) All produce X rays when suddenly stopped.

46. A, B

47. For a S.H. Oscillator, the states possible are

(A) x = 0; v = min; a = 0 (B) x = A; v = 0; a = min
(C) x = 0; v = max; a = 0 (D) x = A; v = 0; a = max

47. C, D

48. When a ray of light enters a denser medium

(A) Its frequency increases (B) Its wavelength decreases
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(C) Its velocity decreases (D) It may suffer a total internal reflection

48. B, C

49. A telescope and a microscope do not differ in respect of

(A) Effective focal length of the system. (B) Method of focussing
(C) Linear magnification (D) None of the above

49. A, C

50. If poloraids are to be used to avoid glares of oncoming light then

(A) Visibility will decrease (B) transmittvity of windshield will decrease
(C) Vehicles will move slowly (D0 cost will increase

50. A, B, D

PART B

B1. (A) A block of mass is kept on smooth horizontal table and is attached to a spring whose other
end is fixed on the table. The block when pulled slightly horizontally and released executes
S.h.M. When its velocity is maximum another block of mass m is placed on it.
Obtain expressions for the ratio of (i) new frequency to the initial frequency (ii) new amplitude
to the initial amplitude

M k
B1. (A) (i) T  2 , 
k M
2 K /(M  m) M
 
1 k /M Mm

(ii) Vel is max at the mean position. V = a, where a is the amplitude
when another mass m is added at the centre. Conservation of momentum gives.
Mv1  (M  m)v 2
v2 M a
  2 2
v1 M  m 1a1
M Mm M
=  =
Mm M Mm

(B) Simplify the following circuit and find the effective capacitance 5 10 5
between X and Y. X
All capacitance is microfarads. 5 10

10
10 10
Y
1. (B) Simplification of circuit in steps gives 5 10 5
X
5 10

10
10 10
Y

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(C) A heater coil boils water in 30 min. Another coil boils the same amount of water in 60 min.
Calculate the time required to boil the same amount of water when the coils are connected in
(i) series (ii) parallel

1. (C) Since total energy required in each case is same

p1p 2
(i) In series total power
p1  p2
2P2  P2 2
=  P2
3P2 3

2
Ts P2  60 P2
3
60  3
Ts   90 min
2

(ii) In parallel total power = P1 + P2 = 3P3

TP3P2 = 60 P2
TP = 20 min.

B2
(A) A wire of length L is wound on a spherical form, and a current I is passed through it. The coil
is then placed in a uniform magnetic field of induction B How many turns should if have for the
torque on it to be maximum? What is the value of this torque?

(B) Two wires of identical dimensions but of difference materials having elastic moduli Y1 and Y2
support a single load from a single support. Find the ratio of the fraction of loads supported by
each wire.

(C) A metal plate (Work function  = 1.2eV) is illuminated by light of  = 4.8  107 m. Calculate
the max velocity of emitted electrons and the stopping potential.

B2. (A) Torque = NABI sin 

Max Torque = NABI for  = 90
For a coil of given length L
Radius = L/2N
L2
Area = (radius) =  
42N2
L2
Torque = NBI 2 2
4 N
l
Torque 
N
 Smallest value of N for max Torque is n = 1
L2BI
 Torque Max =
4

B2 (B) Strings have identical dimensions and they have initial and final lengths (extensions are
also equal) their supporting masses are M1 and M2 then
M gL M gL
Y1  1 2 and Y2  2 2
r e r e
M1 Y1
 
M2 Y2
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 National Standard Examination In Physics -1999-(13)

hc 6.63  10 34  3  108

B2 (C) Incident Energy 
 4.8  107  1.6  10 19
 stopping potential 2.59  1.2 = 1.39  1.4 volt
1.4  1.6  10 19  2
2
v max 
9.1 120 31
2.8  1.6
  10 m/s
2 6
v max
9.1
= 0.7  10 = 7  10 m/s
6 5

B3. (A) A ball weighing 15 gm. is tied to as string 10 cm long. Initially the ball is
held in position such that the string is horizontal such that the string is 15gm
horizontal. The ball is now released. A nail N is situated vertically
below the support at a distance L Calculate the minimum value of L
such that the string will be wound round the nail.

.
(B) A pellet of mercury of radius R breaks into “n” small pellets all of equal radius “r” Show that
the change in energy is given by:
4TR (n 1) where T is the surface tension of mercury.
2 1/3

(C) Show that the increase in the thickness of ice on a pond from initial value x0 to final value x is
given by:
2K
x 2  x 20  t
Lp
Where L = latent heat of fusion; p- density; K = thermal conductivity of ice and (C) is the
temperature of air.

B3. (A) Fro the ball to just take a circular path about n (nail), the string at B 10 cm
must be slack i.e., 15gm
mv 2 B
 mg or v = (Rg) L
R
1  R
also mg, OB =  mv 2   OB = N
2  2 R
C
R
 10 =  2R  R= 4 cm
2
 L = 6 cm

(B) Einitial 4 RT1, Einitial n4RT,

4 3 4
R = n r 3R3 = nr  r = n2R
3

3 3
Change in energy Einitial  E final
= 4 R2 T(n1/ 3  1)

(C) Consider unit area and thickness x of ice.

For increasing thickness of ice of dx1
Heat to be lost by ice = mass  L
= Area  dx  density  L = Ldx

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.
 National Standard Examination In Physics -1999-(14)

KA(2  1 )
Heat conducted = dt (temp of ice = 0C)
x
K.q.{0  ( )}
 dt
x
k
= dt
x
Equating (1) and (2)’
k
Ldx  dt
x
Lxdx
 dt
k
integrating between the limits x0 and x
L x 2  x02
t
K 2
2Kt
 x 2  x 02 
L

B4. (A) A particle is projected making an angle 1 with the horizontal from a point A. It passes through
a point B where its direction of motion makes angle 2 with the horizontal. If the Ist line AB
makes angle  with the horizontal, show that
2 tan  = tan 1 + tan 2

(B) Draw a ray diagram to scale, showing the formation of multiple images by a thick plane mirror

(C) The figure shows electronics transitions between there energy states O
E4
E1, E2 and E3 and the emitted wave lengths
E3
Find in terms of 1 and 2 2
E2

1

E1
4. (A) u sin 2 = u sin 1  gt
u cos 2 = u cos 1
(u sin 2) = (u sin 1) + 2(g)BC
2 2

(u sin 2 )2  (u sin 1 )2
BC 
2g
v sin 2  u sin 1
Also t =
g
AC = u cos 1 t
BC (u sin 2  u sin 1 )(u sin 2  u sin 1 )
tan   
AC g
g
x
(u sin 2  u sin 1 )u cos 1
(u sin 2  u sin 1 )
=
2u cos 1
u sin2 u sin1
2 tan   
u cos 1 u cos 1
using (20 whre u cos 1 = u cos 2 we get
t tan  = tan 2 + tan 1
B4. (B) B.

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 National Standard Examination In Physics -1999-(15)

(C) v1 = C/1
V2 = C/2
v = C/
hv1 + hv2 = hv
hc hc hc
 
1  2 
1 1 1
 
1  2 
1 2

1   2
B5. (A) A body weights W 1 in a liquid of density d1 and W 2 in another liquid density d2. Find the
density of the material of the body.

(B) Two free positive charges 4q and q are situated at a distance “d”. Find the position &
magnitude of third charge that will keep the system in equilibrium.

(C) A tank is filled with water by the inlet A at the rate and is A
siphoned by an outlet B at the rate R2 if R1 < R2 such that A < B
B. Draw graph showing variation of height h with respect to
time. (Tank is empty initially (see figure))
h0
h1 h

B5. (A) W 1 = W  vd1

W 2 = W  vd2
V(d1  d2) = (W 1  W 2)
W W(d1  d2 )
 d= =
V (W2  W1 )

(B) For Q to be in equilibrium

4qQ qQ 2
 x d
x2 (d  x)2 3
for equilibrium of 4q (say)
q4q Q4q
 0
d d (2 / 3d)2
2

9Q
q 0
4
4q
Q
9
4q
The third change must be 
9
2
At a distance d from 4q.
3

(C)
h
fast
slow
h

*******
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BENGALURU
.