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

Options

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

Answer

B

Explanation

A solid sphere is rotating in free space, so there is no external torque.
i.e. `tau = 0`
But the rate of change of angular momentum is equal to the torque.
Then, `(dJ)/(dt) = 0 rArr dJ = 0`
or J = constant
But J = `lomega`, if we increase the radius of the sphere, then its moment of inertia `(l = (2)/(5) MR^(2))` increases.
from `J = lomega`, its angular velocity decreases.
Also, we know that rotational kinetic energy `K_(r ) = (J^(2))/(2l)`