A thin horizontal uniform rod `AB` of mass `m` and length `l` can rotate freely about a vertical axis passing through its end `A`. At a certain moment, the end `B` starts experiencing a constant force `F` which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. The angular velocity of the rod as a function of its rotation angle `theta` measured relative to the initial position should be.

Options

A. `sqrt((6F)/(ml)sin phi)`
B. `sqrt((6F)/(ml)cos phi)`
C. `sqrt((8F)/(ml)sin phi)`
D. `sqrt((8F)/(ml)cos phi)`

Answer

A

Explanation

`lalpha=Fl cos theta,alpha=(3F)/(ml) cos theta`
`omega.(d omega)/(d theta)=(3F)/(ml) cos theta`
`int_(0)^(omega)omega.d omega=(3F)/(ml) int_(0)^(phi)cos theta d theta, omega=sqrt((6F)/(ml) sin phi)`