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

Find dimensions of $ \dfrac{A}{B} $ if \[ \left( P + \frac{A^2}{B} \right) + \frac{1}{2}\rho V^2 = \text{constant}, \] where $ P \rightarrow $ pressure, $ \rho \rightarrow $ density, $ V \rightarrow $ speed.

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.

What is the dimensional formula of $ \frac{1}{\mu_0 \epsilon_0} $ (where $ \mu_0 $ is permeability and $ \epsilon_0 $ is permittivity of free space)?

The equation for real gas is given by $ \left( P + \frac{a}{V^2} \right)(V - b) = RT $, where $ P $, $ V $, $ T $, and $ R $ are the pressure, volume, temperature and gas constant, respectively. The dimension of $ ab $ is equivalent to that of:

Match List-I with List-II.

Match List-I with List-II.

List-I
(A) Coefficient of viscosity
(B) Intensity of wave
(C) Pressure gradient
(D) Compressibility

List-II
(I) [ML^-1T^-1]
(II) [MT^-3]
(III) [ML^-2T^-2]
(IV) [M^-1LT²]

The dimensions of a physical quantity $ \epsilon_0 \frac{d\Phi_E}{dt} $ are similar to:

The dimensions of a physical quantity $ \epsilon_0 \frac{d\Phi_E}{dt} $ are similar to [Symbols have their usual meanings]

Match List-I with List-II.

Choose the correct answer from the options given below: