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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThe position vector of a particle in a rotating body with respect to an origin on the fixed rotation axis is \( \mathbf{r} = 2\hat{i} + 3\hat{j}\text{ m} \). If the angular velocity of the body is \( \boldsymbol{\omega} = 5\hat{k}\text{ rad/s} \), the linear velocity \( \mathbf{v} \) of the particle is:
Correct answer · Option D
\( (-15\hat{i} + 10\hat{j})\text{ m/s} \)
Explanation
\( \mathbf{v} = \boldsymbol{\omega} \times \mathbf{r} = (5\hat{k}) \times (2\hat{i} + 3\hat{j}) = 10(\hat{k} \times \hat{i}) + 15(\hat{k} \times \hat{j}) = 10\hat{j} - 15\hat{i} = -15\hat{i} + 10\hat{j}\text{ m/s} \).
