A rod of mass m and length l is sliding against a smooth vertical wall as shown. The speed of the bottom end of the rod at the instant shown is `V_(0)`. The magnitude of angular momentum of the rod about ICR. (instantaneous axis of rotation) at the instant when `theta=30^(@)` is

Options

A. `(1)/(6)mV_(0)l`
B. `(2)/(3)mV_(0)l`
C. `(1)/(12)mV_(0)l`
D. None of these

Answer

C

Explanation

Calculating torque on upper disc (ring element)
`tau=underset(0)overset(R)intmu sigma(2pixdx)gx`
`tau=musigma2pigunderset(0)overset(R)intx^(2)dx = (musigma2pigR^(3))/(3)`
`inttaudt=DeltaLimplies ((musigma2pigR^(3))/3)t=lomega`
`implies (musigma(2pig)R^(3))/(3)t=(sigma(piR^(2))R^(2))/(2)((2omega_(0))/(3))implies t=(omega_(0)R)/(2mug)`