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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA particle is located at position vector \( \mathbf{r} = (3\hat{i} + 2\hat{j} - \hat{k})\text{ m} \) and a force \( \mathbf{F} = (2\hat{i} - 3\hat{j} + 4\hat{k})\text{ N} \) acts on it. The magnitude of the component of the torque acting on the particle along the unit vector \( \hat{u} = \frac{1}{\sqrt{3}}(\hat{i} + \hat{j} + \hat{k}) \) is:
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Correct answer · Option B
\( \frac{22}{\sqrt{3}}\text{ N m} \)
Explanation
Torque \( \boldsymbol{\tau} = \mathbf{r} \times \mathbf{F} = 5\hat{i} - 14\hat{j} - 13\hat{k}\text{ N m} \). Component along \( \hat{u} \) is \( |\boldsymbol{\tau} \cdot \hat{u}| = \left|\frac{5 - 14 - 13}{\sqrt{3}}\right| = \frac{22}{\sqrt{3}}\text{ N m} \).
