List of top Physics Questions on Dimensional Analysis asked in JEE Main

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

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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:

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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.
Angular Impulse
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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.

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











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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:
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 :

If $R , X _{ L }$, and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance Then which of the following is dimensionless :

If the velocity of light \(c\), universal gravitational constant \(G\) and Planck's constant \(h\) are chosen as fundamental quantities The dimensions of mass in the new system is :
Identify the pair of physical quantities which have different dimensions.

An inductor of 0.5 mH, a capacitor of 200 μF and a resistor of 2 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ × 102 Hz