JEE Main 2025 Jan 29 Shift 1, Physics Q21: Angular Momentum, Its Conservation and Angular Impulse

JEE Main2025Jan 29, Shift 1Physics

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 ______.

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Solution

Compute $τ = r \times F$ with $r = \hat{i} + \hat{j} + \hat{k}$ and $F = \hat{i} - \hat{j} + \hat{k} .$

$τ = \hat{i} \hat{j} \hat{k} 111 1 - 11 = \hat{i} (1 \cdot 1 - 1 \cdot (- 1)) - \hat{j} (1 \cdot 1 - 1 \cdot 1) + \hat{k} (1 \cdot (- 1) - 1 \cdot 1) = 2 \hat{i} + 0 \hat{j} - 2 \hat{k} .$

The $z$ -component is $- 2$ , with magnitude $2 N m .$

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JEE Main 2025 Jan 29 Shift 1, Physics Q21: Angular Momentum, Its Conservation and Angular Impulse

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