A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere ?
Rotational kinetic energy
Moment of inertia
Angular velocity
Angular momentum
As we have learned
Rotational angular momentum -
- wherein
= Moment of inertia about fixed axis of rotation
= angular velocity of rotation
,
Law of conservation of angular moment -
- wherein
If net torque is zero
i.e.
angular momentum is conserved only when external torque is zero .
when we have incraese radius of sphere keeping the mass same then moment of inertia increases
since there is no torque acting since it is rotating freely , angular momemntum remains constant
L = constant , I increases w decreases
Option 1)
Rotational kinetic energy
This is incorrect
Option 2)
Moment of inertia
This is incorrect
Option 3)
Angular velocity
This is incorrect
Option 4)
Angular momentum
This is correct