Mechanics Test

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Mechanics Test - 2

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Question 1
1 / -0

Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimensions of permeability are

A
[M^-1LT^-2A]

B
[ML^-2A^-1]

C
[MLT^-2A^-2]

D
[MLT^-1A^-1]

Solution
Question 2
1 / -0

What is the dimensional formula of Planck's constant?

A
[ML²T^-1]

B
[M^-1LT²]

C
[MLT^-2]

D
[ML²T^-2]

Solution

As the energy is given by,
, where h is the plank's constant and is the frequency, so the dimensional formula of the plank's constant is,
Question 3
1 / -0

What is the dimensional formula of thermal conductivity?

A
[MLT^-1θ^-1]

B
[MLT^-3θ^-1]

C
[M²LT^-3θ^-2]

D
[ML²T^-2θ]

Solution

According to law of thermal conductivity,
[K] =
K = [MLT^-3θ^-1]

Question 4

1 / -0

Match the following:

List - I	List - II
(1) Planck's constant	(A) [ML^-1T^-2]
(2) Gravitational constant	(B) [ML^-1T^-1]
(3) Bulk modulus	(C) [ML²T^-1]
(4) Coefficient of viscosity	(D) [M^-1L³T^-2]

(1) - (C), (2) - (D), (3) - (A), (4) - (B)

(1) - (B), (2) - (A), (3) - (C), (4) - (D)

(1) - (C), (2) - (B), (3) - (A), (4) - (D)

(1) - (C), (2) - (D), (3) - (B), (4) - (A)

Solution

Dimensions of Planck's constant = [ML²T^-1]
Dimensions of gravitational constant = [M^-1L³T^-2]
Dimensions of bulk modulus = [ML^-1T^-2]
Dimensions of coefficients of viscosity = [ML^-1T^-1]
Hence, option (1) is correct.

Question 5
1 / -0

What is the dimensional formula of magnetic field?

A
[MT^-2A^-1]

B
[MT^-1A^-2]

C
[M^-1L^-2TA^-1]

D
[M^-1LTA^-2]

Solution

F = BiLsinθ
B = = [MT^-2A^-1]
Question 6
1 / -0

The time period 't' of a drop of liquid of density 'd' and radius 'r', vibrating under surface tension 's', is given by the formula t = . If a = 1 and c = -1, then b is

A
1

B
2

C
3

D
4

Solution
Question 7
1 / -0

Which of the following quantities is unitless as well as dimensionless?

A
Angle

B
Solid angle

C
Mechanical equivalent of heat

D
Refractive index

Solution

In optics, the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as the ratio of the speed of light in vacuum relative to that in the considered medium. This can be written mathematically as:
n = speed of light in a vacuum/speed of light in a medium
Since refractive index is the ratio of same quantities, so it has no unit and is a dimensionless quantity.
Question 8
1 / -0

In the relation , 'P' is pressure, 'z' is distance, 'k' is Boltzmann constant and 'θ' is temperature. What will be the dimensional formula of β?

A
[M⁰L²T⁰]

B
[ML²T]

C
[ML⁰T^-1]

D
[ML²T^-1]

Solution
Question 9
1 / -0

If e, ε₀, h and c respectively are electronic charge, electric permittivity, Planck's constant and velocity of light in vacuum, then what are the dimensions of ?

A
[M⁰L⁰T⁰]

B
[ML⁰T⁰]

C
[M⁰LT⁰]

D
[M⁰L⁰T]

Solution

[e²] = [Q²] = [A²T²]
[] = [M^-1L^-3T⁴A²]
[h] = [ML²T^-1]
[c] = [LT^-1]
=
= [M⁰L⁰T⁰]
Question 10
1 / -0

The pair(s) of physical quantities that do(es) not have the same dimensions is/are

A
Reynolds number and coefficient of friction

B
Curie and frequency of a light wave

C
Latent heat and gravitational potential

D
Planck's constant and torque

Solution

Reynolds number and coefficient of friction are dimensionless quantities.
Curie is the number of atoms decaying per unit time and frequency is the number of oscillations per unit time. Latent heat and gravitational potential both have the same dimensions corresponding to L²T^-2.
Question 11
1 / -0

In an experiment, the values of two resistances were measured as R₁ = 5 ± 0.2 ohm and R₂ = 10 ± 0.1 ohm. What is their combined resistance in series?

A
[15 ± 2%]

B
[10 ± 6%]

C
[5 ± 7%]

D
[4 ± 8%]

Solution

In series, R .

In terms of percentage, we have

%

Value of the combination of resistance in series is 15 ± 2%
Question 12
1 / -0

If force (F), work (W) and velocity (v) are taken as fundamental quantities, then what is the dimensional formula of time (T)?

A
[WFv]

B
[WFv^-1]

C
[W^-1F^-1v]

D
[WF^-1v^-1]

Solution

Work done = Force × distance

As distance = Velocity × time

∵ V =
W = F.V.t

∴ T =
∴ [T] = [WF^-1V^-1]
Question 13
1 / -0

What are the dimensions of 'a' in the van der Waals' equation?

A
[M¹L^-1T^-2]

B
[M¹L⁵T^-2]

C
[M¹L³T^-2]

D
[M¹L²T^-2]

Solution

According to the principle of homogeneity of dimension, only like quantities can be added or subtracted.
van der Waals' eqauation is

Here, Dimensions of = Dimensions of P,
Dimensions of a = Dimensions of [PV²]
= [M¹L^-1T^-2] [L³]²= [M¹L⁵T^-2]
Question 14
1 / -0

Directions: The following question has four choices out of which ONLY ONE is correct.

The dimensions of universal gas constant are:

A
[ML²T^-2θ^-1]

B
[M²LT^-2θ]

C
[ML³T^-1θ^-1]

D
None of these

Solution

PV = nRT
Question 15
1 / -0

Which of the following sets of quantities has the same dimensional formula?

A
Frequency, angular frequency and angular momentum

B
Surface tension, stress and spring constant

C
Acceleration, momentum and retardation

D
Work, energy and torque

Solution

As the work is defined as the dot product of force and displacement.
Torque is represented as the cross product of radius and the force.
Energy is defined as the capacity of doing work so work, energy and the torque has same dimensions.