Question

Consider the following two statements, A and B and identify the correct choice:
A) The torque required to stop a rotating body in a given time is directly proportional to its initial angular momentum.
B) If radius of earth shrinks, then its rotational kinetic energy increases.

• A. A is True but B is False
• B. A is False but B is True
• C. Both A and B are True
• D. Both A and B are False

Answer 1

The correct option is C Both A and B are True

A. $\omega ={\omega }_0-\alpha t$
$\alpha =\frac{({\omega }_0-\omega )}{t}$
$T=I\alpha =\frac{I({\omega }_0-\omega )}{t}=\frac{L_0-L}{t}$
$\therefore T\propto L_0$
$\left(B\right)$ Since there is no external torque,
$L=I\omega =constant$
$\therefore I\propto \frac{1}{\omega }$
On decreasing the radius, the moment of inertia decreases and hence, $\omega$ will increase.
$KE=\frac{1}{2}I{\omega }^2=\left(\frac{1}{2}I\omega \right)\times \omega =\left(constant\right)\times \omega$
Therefore, KE will also increase on decreasing the radius