A rigid body is rotating about a vertical axis. In t second, the axis gradually becomes horizontal. But the rigid body continues to make v rotations per second throughout the time interval of 1 second. If the moment of inertia I of the body about the axis of rotation can be taken as constant, then the torque acting on the body is

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$2 πv$

$\frac{2 \sqrt{2} πv}{t}$

$2 \sqrt{2} πv$

$\frac{2 \sqrt{2} πvl}{t}$

answer is D.

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Detailed Solution

$\begin{array}{l} \vec{τ} = I \vec{α} or \vec{τ} = \frac{I ({\vec{ω}}_{2} - {\vec{ω}}_{1})}{t} \\ But |ω_{2} - {\vec{ω}}_{1}| = \sqrt{ω_{2}^{2} + ω_{1}^{2}} = \sqrt{2} ω = \sqrt{2} \times 2 πv \\ τ = \frac{I}{t} \times 2 \sqrt{2} πv (or) \\ τ = \frac{2 \sqrt{2} πvI}{t} \end{array}$