WS 11th CH 1 - UNITS & DIMENSIONS 2023-24

ASSIGNMENT 1 (Session: 2023-24)
SUBJECT:PHYSICS (Ch-1) CLASS : XI
TOPIC : Units and Measurements
Very short Answer Type Questions
1.Which of the following pairs has the same dimensions?

(a) specific heat and latent heat (b) lmpulse and momentum
(c) surface tension and force (d) moment of lnertia and torque
2. Physical quantities are

(a) quantities such as degrees, radians and steradians
(b) quantities such as length, mass, time, electric current, thermodynamic temperature, amount of
substance, and luminous intensity
(c) quantities such as pounds, dollars and rupees
(d) quantities such as kilos, pounds and gallons
3.If force (F), work (W) and velocity (v) are taken as fundamental quantities. What is the
dimensional formula of time (T)?
(a) [WFv] (b) [WFv-1] (c) [W-1F -1v] (d) [WF-1v -1]
4. Which of the following groups have different dimensions?

(a) Potential difference, EMF, voltage (b) Pressure, stress, Youngs modulus
(c) Heat, energy, work done (d) Dipole moment, electric flux, electric
field
5. Electron volt is a unit of

(a) charge (b) potential difference (c) energy (d) magnetic force
6. Which quantity can be written in SI units in kgm2A-2s-3?
7. Write two pair of quantities which have the same dimensions.
8. How the physical quantities can be divided on the basis of dimensions.
9. Give the number of significant figure
(1) 1000.002 (2) 0.23x10-23

10. Can a physical quantity has dimension but still have no units.?
11. The density of the material is 2.1g cm-3. Express it in Kg m-3
12. The radius of the atom is 1A0 and the radius of the nucleus is 1 fm. How magnitudes higher
is the volume of atom as compared to the volume of the nucleus.
13. If ‘slap’ times speed equals power, what will be the dimensional equation for ‘slap’?
Short Answer Type ( 2/3 Marks Questions)
14. A laser is beamed towards a planet from earth and its echo is received 680 s latter. If
distance of planet be 1.02x1011 m, what is the speed of laser light ?
15. Find the value of 60W on a system having 100g, 20cm and1minute as the fundamental
Units.
B
16.When white light travels through glass µ =A + using the principle of homogeneity. Find
λ2
the dimension of constant A and B.
17. The density of a material in CGS system of units is 4g/cm2.In a system of units in which unit
of length is 10cm and unit of mass is 100g.Find the value of density.
18. If the velocity of light c , the constant of gravitation G and plank constant h be chosen as
fundamental units , find the dimension of mass , length, and time in terms
19. A simple harmonic oscillator has a mass m, amplitude A, frequency v, displacement x and
2 2
kinetic energy E. The equation is E=2 v m (A - x). Is this dimensionally correct?
20. If x = a + bt + ct 2 where x is in metres and t in seconds, write the units of a, b, c.
21. If Energy, velocity & Time are the fundamental units, find the dimension of surface tension?
22. If a unit of force, velocity & energy are 100 dyne, 10 cm/s & 400 ergs. What will be units of
mass, length and time?
23. Force (F) & density (d) are related as : F= A /( B +√d). Find the dimensions of A & B.
24. In Vander Wall’s equation ( P + a/V 2 )( V – b ) = RT, Determine the dimensions of a and b..
25.. If E, M, J and G respectively denote energy, mass, angular momentum and gravitational
constant, Calculate the dimensions of EJ 2 /M 5 G 2
26. Assuming that the mass (m) of a stone that can be moved with flowing water depends only
on the velocity v, the density d of water & amp; g. Show that m varies with the sixth power of
the velocity of FLOW.
27.Reynolds number N determines the condition of laminar flow of a liquid through a pipe. N is
function of average speed v, the coefficient of viscosity h and the density of the liquid r. Given
that N is directly proportional to the diameter of the pipe. Show by dimensional analysis that
N =µ rvd/h
28. A large fluid star oscillate in shape under the influence of its own gravitational field
Using the dimension analysis , find the expression for the period of oscillation (T) in terms of
radius of star (R), mean density of fluid (ρ) and universal gravitational constant( G).
29. The number of particles are given by n=-D (n2 - n1)/(x2-x1) are crossing the unit are
perpendicular to the X-axis in unit time, n1 and n2 are the number of particles per unit
volume for the values of x meant to be x1 and x2. What is the dimensional formula for the
diffusion constant D?
CASE STUDY
The van-der Waals equation is
Q.1 The dimensional formula for b is same as that for
(A) P (B) V (C) PV2 (D) RT
Q.2 The dimensional formula for a is same as that for
(A) V2 (B) P (C) PV2 (D) RT
Q.3 Which of the following does not possess the same dimensional formula as that for RT?
(A) PV (B) Pb (C) a/V2 (D) ab/V2
Q.4 The dimensional formula for ab/RT is
(A) M L5 T-2 (B) M0 L3 T0 (C) M L-1 T-2 (D) M0L6T 0

Q.5 The dimensional formula of RT is same as that of
(A) Energy (B) Force
(C) Specific heat (D) Latent heat
II
Significant figures in the measured value of a physical quantity tell the number of digits in which
we have confidence .Larger the number of significant figures obtained in a measurement , greater
is the accuracy of measurement and vice – versa . In addition or subtraction, the number of
decimal places in the result should equal the smallest number of decimal places in any term in
the operation .
In multiplication and division , the number of significant figures in the product or in the quotient
is the same as the smallest number of significant figures in any of the factors.
With the help of above comprehension, choose the most appropriate alternative for each of the
following questions:
Q1. The area enclosed by a circle of diameter 1.06 m with correct number of significant figures
is
(a) 0.88m2 (c) 1.88m2
(b)0.883m2 (d) 0.882026m2
Q2. The circumference of the circle of diameter 1.06 m with correct number of significant
figures is
(a) 3.33m (c) 3.3m
(b)3.33142m (d) 3m
Q3. Subtract 2.6x 104 from 3.9x 105 with due regard to significant figures.
(a) 3.64x105 (c) 3.6 x105
(b) 3.7x105 (d) 3.65 x 106
Q4. Add 3.8x 10-6 to 4.2 x 10-5 with due regard to significant figures.
(a) 4.6 x10-5 (c) 4.58 x10-5
(b) 4.6x10-6 (d) 4.580 x 10-5

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ASSIGNMENT 1 (Session: 2023-24)

SUBJECT:PHYSICS (Ch-1) CLASS : XI

TOPIC : Units and Measurements

Very short Answer Type Questions

1.Which of the following pairs has the same dimensions?

2. Physical quantities are

4. Which of the following groups have different dimensions?

5. Electron volt is a unit of

6. Which quantity can be written in SI units in kgm2A-2s-3?

7. Write two pair of quantities which have the same dimensions.

8. How the physical quantities can be divided on the basis of dimensions.

9. Give the number of significant figure

(1) 1000.002 (2) 0.23x10-23

11. The density of the material is 2.1g cm-3. Express it in Kg m-3

Short Answer Type ( 2/3 Marks Questions)

distance of planet be 1.02x1011 m, what is the speed of laser light ?

20. If x = a + bt + ct 2 where x is in metres and t in seconds, write the units of a, b, c.

The van-der Waals equation is

Q.1 The dimensional formula for b is same as that for

(A) P (B) V (C) PV2 (D) RT

Q.2 The dimensional formula for a is same as that for

(A) V2 (B) P (C) PV2 (D) RT

(A) PV (B) Pb (C) a/V2 (D) ab/V2

Q.4 The dimensional formula for ab/RT is

(A) M L5 T-2 (B) M0 L3 T0 (C) M L-1 T-2 (D) M0L6T 0

(A) Energy (B) Force

(C) Specific heat (D) Latent heat

(a) 0.88m2 (c) 1.88m2

(b)0.883m2 (d) 0.882026m2

(a) 3.33m (c) 3.3m

(a) 3.64x105 (c) 3.6 x105

(b) 3.7x105 (d) 3.65 x 106

(a) 4.6 x10-5 (c) 4.58 x10-5

(b) 4.6x10-6 (d) 4.580 x 10-5

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