List of top Physics Questions on Dimensional Analysis

Dimensions of $G$ (Universal gravitational constant) in terms of $h$ (Planck's constant), $m$ (mass), $t$ (time) and $L$ (length) will be:

Match the LIST-I with LIST-II

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Match the LIST-I with LIST-II:

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Given a charge $ q $, current $ I $ and permeability of vacuum $ \mu_0 $. Which of the following quantity has the dimension of momentum?

The pair of physical quantities not having the same dimensions is:

The dimensions of $ (\mu \epsilon)^{-1} $, where $ \epsilon $ is permittivity and $ \mu $ is permeability of a medium, are:

The dimensional formula of magnetic permeability $\mu_0$ is:

Match List-I with List-II.

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The expression given below shows the variation of velocity $ v $ with time $ t $: \[ v = \frac{At^2 + Bt}{C + t} \] The dimension of $ A $, $ B $, and $ C $ is:

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:

Match List - I with List - II.

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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 - I	List - 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} $

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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:

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:

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:

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 :

List - I	List - 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) \( M L^2 T^{-1} \)