A particle of mass `m` moving with velocity `V_(0)`stick a simple pendulum of mass `m` and stick to it. The maximum height attained by the pendulum will be

Options

A. `h=(V_(0)^(2))/(8g)`
B. `sqrt(V_(0)g)`
C. `2sqrt((V_(0))/(g))`
D. `(V_(0)^(2))/(4g)`

Answer

A

Explanation

Initial momentum of particle `= mV_(0)`
Final momentum of system (particle + pendulum) = 2mv
By the law of conservation of momentum
`rArr mV_(0)=2mv rArr` Initial velocity of system `v = (V_(0))/(2)`
`therefore` Initial K.E. of the system `= (1)/(2)(2m)v^(2) = (1)/(2)(2m)((V_(0))/(2))^(2)`
If the system rises up to height h then P.E. =
By the law of conservation of energy
`(1)/(2)(2m)((V_(0))/(2))^(2)=2mgh rArr h = (V_(0)^(2))/(8g)`