JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Rotational Mechanics

The torque due to the force

(2 \hat{i} + \hat{j} + 2 \hat{k})

about the origin, acting on a particle whose position vector is

(\hat{i} + \hat{j} + \hat{k})

, would be

(A) $\hat{i} - \hat{j} + \hat{k}$
(B) $\hat{i} + \hat{k}$
(C) $\hat{i} - \hat{k}$ ✓ Correct
(D) $\hat{j} - \hat{k}$

Answer: (C)

Solution

Torque about the origin is

τ = r \times F

, with

r = \hat{i} + \hat{j} + \hat{k}

and

F = 2 \hat{i} + \hat{j} + 2 \hat{k}

τ = \hat{i} 12 \hat{j} 11 \hat{k} 12 = \hat{i} (1 \cdot 2 - 1 \cdot 1) - \hat{j} (1 \cdot 2 - 1 \cdot 2) + \hat{k} (1 \cdot 1 - 1 \cdot 2)

= \hat{i} (1) - \hat{j} (0) + \hat{k} (- 1) = \hat{i} - \hat{k}

JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Single correct option

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