List of top Physics Questions on Dimensional Analysis

Acceleration due to gravity on the surface of earth is \( g \). If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________________ g.
In a measurement, it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of \( [M^a L^b T^c] \). If \( b = 3 \), the value of \( c \) is:
Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T, and C stand for unit of mass, length, time, and charge.

Match List - I with List - II. 

List - IList - II
(A) Latent Heat(I) \( M^0 L^2 T^{-2} \)
(B) Electromotive Force(II) \( M L^2 T^{-3} A^{-1} \)
(C) Electrical Resistivity(III) \( M L^3 T^{-3} A^{-2} \)
(D) Angular Impulse(IV) \( M L^2 T^{-1} \)











Choose the correct answer from the options given below:

Acceleration due to gravity on the surface of earth is \( g \). If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is \_\_\_\_ g.
The coordinates of a particle with respect to origin in a given reference frame is \( (1, 1, 1) \) meters. If a force of \( \mathbf{F} = \hat{i} - \hat{j} + \hat{k} \) acts on the particle, then the magnitude of torque (with respect to origin) in \( z \)-direction is:

While determining the coefficient of viscosity of the given liquid, a spherical steel ball sinks by a distance \( x = 0.8 \, \text{m} \). The radius of the ball is \( 2.5 \times 10^{-3} \, \text{m} \). The time taken by the ball to sink in three trials are tabulated as shown: 

If the dimensions of length are expressed as \( G^x C^y h^z \), where \( G \), \( C \), and \( h \) are the universal gravitational constant, speed of light, and Planck's constant respectively, then:

A quantity \( X \) is given by: \[ X = \frac{\epsilon_0 L \Delta V}{\Delta t} \] where:
- \( \epsilon_0 \) is the permittivity of free space,
- \( L \) is the length,
- \( \Delta V \) is the potential difference,
- \( \Delta t \) is the time interval.
The dimension of \( X \) is the same as that of:

The dimensional formula of Planck’s constant is
Dimensions of the physical quantity $X$ in the equation \[ {Force} = \frac{X}{{Volume}} \] are
The number of significant figures in 0.0500L is
In the measurement of length 6 $\mu$m is equal to $x$ pm. Then the value of $x$ is
Kirchhoff’s junction rule is based on conservation of

Choose the INCORRECT dimensions:

What is the dimensional formula of \( ab^{-1} \) in the equation \[ \left( P + \frac{a}{V^2} \right) (V - b) = RT, \] where letters have their usual meaning.
If \( \epsilon_0 \) is the permittivity of free space and \( E \) is the electric field, then \( \epsilon_0 E^2 \) has the dimensions:
The dimensional formula of latent heat is:
If G be the gravitational constant and u be thee nergy density then which of the following quantity have the dimension as that the \(\sqrt{UG}\)
The dimensional formula of angular impulse is :
The dimensions of angular impulse is equal to :
Time dependence of quantity \(P=P_0 e^{-a t^2}\), dimension of a is

E, m, L, G represent energy, mass, angular momentum and gravitational constant respectively. The dimensions of \[ \frac{EL^2}{mG^2} \] will be that of 

The dimensional formula of kinetic energy is equal to which of the following?
Which of the given dimensional formula represents heat capacity?