Question

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass the same. Which of the following physical quantities would remain constant for the sphere?
(1) Angular velocity
(2) Moment of inertia
(3) Rotational kinetic energy
(4) Angular momentum

Answer 1

Hint: The sphere was initially rotating freely about an axis passing through its centre of mass and the axis of rotation. Now suddenly radius of sphere is increased while keeping all other quantities same, in this process no external torque acts on the system

Complete step by step answer:
In this process on the system no external force acts on the system, hence net torque acting on the system is zero. Now we know the relationship between torque and angular momentum is given by,
\[\dfrac{dL}{dt}=\tau \],
Since \[\tau =0\], this means that angular momentum is constant.
So, by conservation of angular momentum, total momentum before collision must be equal to the total momentum after collision.
Momentum before collision= momentum after collision
\[{{L}_{1}}={{L}_{2}}\]
Therefore, taking the same mass of sphere, if radius is increased, then moment of inertia, rotational kinetic energy and angular velocity will change but according to law of conservation of momentum, angular momentum will not change.

Hence the correct option is (4).

Note:Also, we have to take the moment of inertia of the body given, we should keep in mind different bodies have different moments of inertia. Also, the moment of inertia depends upon the axis of rotation around which it is being calculated.