Question

A solid sphere is rotating in free space. If the radius of sphere is increased keeping mass same which one of the following will not be affected?

• A. Angular velocity
• B. Angular momentum
• C. Moment of inertia
• D. Rotational kinetic energy

Answer 1

Answer: (B)

A solid sphere is rotating in free space, so there is no external torque,
ie, $\tau =0$
But the rate of change of angular momentum is equal to the torque
then $\frac{dJ}{dt}=0$
or $dJ=0$
or $J$ = constant
But $J=I\omega$, if we increase the radius of the sphere then its moment of inertia $\left(I=\frac{2}{5}M{R}^2\right)$ increases
From $J=I\omega$, its angular velocity decreases Also we know that the rotational kinetic energy
$K_r=\frac{J^2}{2I}$
Hence, $K_r$ decreases as $I$ is increases