A uniform rod `AB` of length `l` and mass `m` hangs from point `A` in a car moving with velocity `v_(0)` on an inclined plane as shown in Fig. The rod can rotate in vertical plane about the axis at point `A`. if the car suddenly stops, the angular speed with which the rod starts rotating is

Options

A. `3/2(v_(0))/l cos theta`
B. `(v_(0))/2 (costheta)/l`
C. `3/2(v_(0))/lsintheta`
D. `5/2(v_(0))/lsintheta`

Answer

A

Explanation

When the car is moving with the constant speed, the rod will be vertical. The centre of mass of the rod is moving with a velocity `v_(0)` parallel to the plane. Conserving agular momentum about `A`, we get
`mv_(0)l/2costheta=(ml^(2))/3omegaimplies omega=3/2v_(0)/lcostheta`