Question

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 $1s$. 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 :

• A. $2\pi v$
• B. $2\sqrt{2}\pi v$
• C. $\frac{2\sqrt{2}\pi v}{t}$
• D. $\frac{2\sqrt{2}\pi vl}{t}$

Answer 1

The correct option is D $\frac{2\sqrt{2}\pi vl}{t}$

$\overrightarrow{\tau }=I\overrightarrow{\alpha }$ or $\overrightarrow{\tau }I=\frac{I(\overrightarrow{{\omega }_2}-\overrightarrow{{\omega }_1})}{t}$
But $|{\omega }_2-\overrightarrow{{\omega }_1}|=\sqrt{{\omega }_2^2+{\omega }_1^2}=\sqrt{2}\omega =\sqrt{2}\times 2\pi v$
$\tau =\frac{I}{t}\times 2\sqrt{2}\pi v$ or $\tau =\frac{2\sqrt{2}\pi vI}{t}$