The coordinates of a particle with respect to origin in a given reference frame is $(1,1,1)$ meters. If a force of $\vec{F}=\hat{i}-\hat{j}+\hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z -direction is $\_\_\_\_$ .

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Rotational Mechanics

The coordinates of a particle with respect to origin in a given reference frame is

(1, 1, 1)

meters. If a force of

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

acts on the particle, then the magnitude of torque (with respect to origin) in z -direction is

____

Answer: 2

Solution

Torque about the origin is

τ = r \times F

, with

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

and

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

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

= \hat{i} (2) - \hat{j} (0) + \hat{k} (- 2) = 2 \hat{i} - 2 \hat{k}

The z-component of torque has magnitude 2 N·m.

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Integer answer

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