Two small rings O and O' are put on two vertical stationary rods AB and A'B', respectively. One end of an inextensible thread is tied at point A'. The thread passes through ring `O'` and its other end is tied to ring O. Assuming that ring O' moves downwards at a constant velocity `v_(1)`, then velocity `v_(2)` of the ring O, when `/_AOO'=alpha` is

Options

A. `v_(1)[(2 sin^(2)alpha//2)/(cos alpha)]`
B. `v_(1)[(2 sin^(2)alpha//2)/(sin alpha)]`
C. `v_(1)[(3 sin^(2)alpha//2)/(sin alpha)]`
D. None of these

Answer

A

Explanation

`v_(2) cos alpha + v_(1) cos alpha = v_(1) implies v_(2)=v_(1)[(2 sin^(2)(alpha//2))/(cos alpha)]`.