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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA force \( \mathbf{F} = (a\hat{i} + 3\hat{j} + 6\hat{k})\,\text{N} \) is acting at a point whose position vector is \( \mathbf{r} = (2\hat{i} - 6\hat{j} - 12\hat{k})\,\text{m} \). The value of \( a \) for which angular momentum about the origin is conserved is:
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Correct answer · Option A
\( -1 \)
Explanation
For angular momentum to be conserved, torque \( \boldsymbol{\tau} = \mathbf{r} \times \mathbf{F} = 0 \), meaning \( \mathbf{F} \) must be parallel or antiparallel to \( \mathbf{r} \). Thus, \( \frac{a}{2} = \frac{3}{-6} = \frac{6}{-12} = -\frac{1}{2} \implies a = -1 \).
