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

If angular position of a particle is given by $\theta = \frac{t^4}{4} + t^2$. Find angular acceleration at $t = 1s$:

The dimension of $\frac{1}{2} \epsilon_0 E^2$ is $M^a L^b T^c$ then value of $a - 2b + c = ?$

In Searl's experiment diameter of wire is measured with screw gauge of least count $0.001 \text{ cm}$ and its value is $0.08 \text{ cm}$. Length of wire is $150 \text{ cm}$ with least count $0.1 \text{ cm}$ and elongation $0.5 \text{ cm}$ with least count $0.001 \text{ cm}$. Weight suspended is $100 \text{ N}$ then absolute error in Young's modulus is $N \times 10^9 \text{ N/m}^2$. Then $N$ is :

A satellite is revolving around planet of mass $2M$ in orbit of radius $R$ with time period is $T_1$. Another satellite is revolving around planet of mass $4M$ in orbit of radius $2R$, with time period $T_2$. Find $\frac{T_1}{T_2}$.

A particle is moving such that its velocity vector at co-ordinate $(x,y,z)$ is $\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k}$. Find magnitude of acceleration at $(1,1,4)$.

If stress at $x = \ell/3$ from bottom is $\frac{W}{A} + \frac{2}{\gamma} \frac{w}{A}$ then find $\gamma$ :

If $\vec{r} = 10t^2 \hat{i} + 5t^3 \hat{j}$ and mass of object, $m = 0.1 \text{ kg}$ then at $t = 1 \text{ sec}$ :-
(A) momentum = $2\hat{i} + 1.5\hat{j}$
(B) force = $2\hat{i} + 3\hat{j}$
(C) Angular momentum = $5\hat{k}$
(D) Torque = $20\hat{k}$

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: