In the figure shown, the instantaneous speed of end `A` of the rod is `v` to the left. The angular velocity of the rod of length `L` must be

Options

A. `v/(2L)`
B. `v/L`
C. `(vsqrt(3))/(2L)`
D. none of these

Answer

B

Explanation

The velocities of the ends `A` and `B` along the length of rod should be the same.
Hence `v_(A)cos30^@=v_(B)cos30^@implies v_(A)=v_(B)=v`
Hence the angular velocity of the rod is
`omega=((v_(AB))_(_|_))/l=(2vsin30^@)/limpliesomega=v/l`