Two small rings `O` and `O'` are put on two vertical stationery 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)`, determine the velocity `v_(2)` of the ring `O`, when `/_AOO'=alpha`.

Options

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

Explanation

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