JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Chapter_pending

Match List-I with List-II.

Choose the correct answer from the options given below :

Answer: A → II, B → IV, C → I, D → III

Solution

Each entry follows from expressing the quantity in terms of mass, length and time.

Young's modulus:

Y = \frac{F / A}{Δ ℓ / ℓ}

, so

[Y] = \frac{M L T ^{- 2}}{L ^{2}} = M L^{- 1} T^{- 2}

→ (II)

Torque:

τ = r \times F

, so

[τ] = L \cdot M L T^{- 2} = M L^{2} T^{- 2}

→ (IV)

Coefficient of viscosity, from

F = η A \frac{d v}{d x}

[η] = \frac{M L T ^{- 2}}{L ^{2} \cdot ( L T ^{- 1} / L )} = M L^{- 1} T^{- 1}

→ (I)

Gravitational constant, from

F = \frac{G M _{1} M _{2}}{r ^{2}}

[G] = \frac{M L T ^{- 2} \cdot L ^{2}}{M ^{2}} = M^{- 1} L^{3} T^{- 2}

→ (III)

So (A)-(II), (B)-(IV), (C)-(I), (D)-(III).

JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Match the columns