List of top Physics Questions on Dimensional analysis

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. 

The dimensions of the area \( A \) of a black hole can be written in terms of the universal constant \( G \), its mass \( M \), and the speed of light \( c \) as \( A = G^\alpha M^\beta c^\gamma \). Here

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.
Young’sModulus:
Choose the correct answer from the options given below:
What is the dimensional formula of the energy density of an electromagnetic wave?
What are the units of the constant in the above equation?