JEE Physics 2025 Question with Solution

Given: A match-the-following question on dimensional analysis.

Find: The correct option for matching the physical quantities with their dimensional formulas.

From the solution:

• Young's Modulus is stress/strain, so its dimension is

$$\frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2}$$

• Torque is force $\times$ distance, so its dimension is

$$MLT^{-2} \times L = ML^2T^{-2}$$

• Coefficient of Viscosity is obtained from

$$\eta = \frac{\text{Force/Area}}{\text{Velocity gradient}} = \frac{ML^{-1}T^{-2}}{T^{-1}} = ML^{-1}T^{-1}$$

• Gravitational Constant from Newton's law has dimension

$$G = \frac{Fr^2}{m_1 m_2} = \frac{(MLT^{-2})L^2}{M^2} = M^{-1}L^3T^{-2}$$

the solution explicitly states: The Correct Option is D.

It also notes the final matching as

$$(A)-(I), \; (B)-(II), \; (C)-(I), \; (D)-(IV)$$

which does not exactly match the listed options. Since the solution explicitly declares option D as correct, the answer is taken as D in accordance with the solution.

Therefore, the correct option is D.

Given: The quantities are to be matched using their dimensional formulas.

Find: Which option among A, B, C, D is marked correct by the solution.

The extracted working shows:

1. Young's Modulus

$$\text{Young's Modulus} = \frac{\text{Stress}}{\text{Strain}}$$

Since strain is dimensionless and stress is force per area,

$$\text{Stress} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2}$$

So Young's Modulus corresponds to $ML^{-1}T^{-2}$.

2. Torque

$$\text{Torque} = \text{Force} \times \text{distance}$$

Hence,

$$MLT^{-2} \times L = ML^2T^{-2}$$

So Torque corresponds to $ML^2T^{-2}$.

3. Coefficient of Viscosity Using

$$\eta \frac{dv}{dy} = \frac{\text{Force}}{\text{Area}}$$

we get

$$\eta = \frac{ML^{-1}T^{-2}}{T^{-1}} = ML^{-1}T^{-1}$$

So the coefficient of viscosity corresponds to $ML^{-1}T^{-1}$.

4. Gravitational Constant From

$$F = G\frac{m_1m_2}{r^2}$$

we obtain

$$G = \frac{Fr^2}{m_1m_2} = \frac{(MLT^{-2})L^2}{M^2} = M^{-1}L^3T^{-2}$$

So gravitational constant corresponds to $M^{-1}L^3T^{-2}$.

The solution text contains an internal inconsistency: the dimensional matching written in the steps does not align cleanly with the listed options, and one portion even says "Thus, the correct answer is option (4)." However, the solution clearly states The Correct Option is D.

Therefore, using the solution, the correct option is D.