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

Options

A. `mgrt cos theta`
B. `mgrt sin theta`
C. `(3//2) mgrt sin theta`
D. none of these

Answer

B

Explanation

(b) Since the surface is frictionless, the body does not ratate about its centre of mass. Only it slides parallel to the surface. i.e., `omega = 0` and `v (g sin theta) t`
The angular momentum after time `t` :
`L = mvr = m(g sin theta t) r = mgrt sin theta`.