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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThe position vector of a particle of mass \( 2\text{ kg} \) moving in the \( xy \)-plane varies with time as \( \mathbf{r}(t) = (2t^2\hat{i} + 3t\hat{j})\text{ m} \). The magnitude of the torque acting on the particle about the origin at \( t = 2\text{ s} \) is:
Correct answer · Option 1
\( 48\text{ N m} \)
Explanation
\( \mathbf{v} = 4t\hat{i} + 3\hat{j} \), \( \mathbf{a} = 4\hat{i} \), hence \( \mathbf{F} = m\mathbf{a} = 8\hat{i}\text{ N} \). At \( t = 2\text{ s} \), \( \mathbf{r} = 8\hat{i} + 6\hat{j}\text{ m} \). Torque \( \boldsymbol{\tau} = \mathbf{r} \times \mathbf{F} = (8\hat{i} + 6\hat{j}) \times 8\hat{i} = -48\hat{k}\text{ N m} \), magnitude is \( 48\text{ N m} \).
