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

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
rotation
The angular momentum after a time t is given as
L = mvr
L = m(gsinθt) r
L = mgrt sinθ

Author: Rajesh Jha

QuantumStudy.com for CBSE|IIT-JEE|NEET

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