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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA particle moves in the \( xy \)-plane under the action of a constant force \( \vec{F} = 4\hat{i}\text{ N} \). At time \( t \), its position vector is \( \vec{r}(t) = (2t^2\hat{i} + 3t\hat{j})\text{ m} \). The torque \( \vec{\tau} \) of this force about the origin at \( t = 2\text{ s} \) is:
Correct answer · Option 2
\( -24\hat{k}\text{ N}\cdot\text{m} \)
Explanation
At \( t = 2\text{ s} \), \( \vec{r} = 8\hat{i} + 6\hat{j} \). Torque \( \vec{\tau} = \vec{r} \times \vec{F} = (8\hat{i} + 6\hat{j}) \times (4\hat{i}) = 24(\hat{j} \times \hat{i}) = -24\hat{k}\text{ N}\cdot\text{m} \).
