Q: A body of mass m and radius r is released from rest along a smooth inclined plane of angle of inclination θ . The angular momentum of the body about the instantaneous point of contact after a time t from the instant of release is equal to

(A) mgrt cosθ

(B) mgrt sinθ

(C) (3/2) mgrt sinθ

(D) None of these

Solution : Since the surface is frictionless , the body does not rotate about its centre of mass. Only it slides with certain velocity v parallel to the surface

Hence,ω = 0 & v = (g sinθ) t

The angular momentum after a time t is given as

L = mvr

L = m(gsinθt) r

L = mgrt sinθ