Q. A solid homogeneous sphere is moving on a rough horizontal surface partly rolling and partly sliding. During this kind of motion of the sphere
A) Total kinetic energy is conserved
B) The angular momentum of the sphere about the point of contact with the plane is conserved
C) Only the rotational kinetic energy about the centre of mass is conserved
D) Angular momentum about the centre of mass is conserved
Explanation
(b) Kinetic energy will not be conserved because friction force is acting at the point of contact with the plane. But torque of this force about point of contact will be zero. So angular momentum of the sphere about point of contact will be conserved
$\overrightarrow{\tau} = \frac{d\overrightarrow{L}}{dt}$, if $\overrightarrow{\tau} = 0$ then $\overrightarrow{L} =$ constant
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.