A shere of mass `m` , moving with velocity `V`, enters a hanging bag of sand and stop. If the mass of the bag is `M` and it is reised by height `h`, then the velocity of the sphere will be

Options

A. `(M + m)/(m) sqrt(2 gh)`
B. `(M)/(m) sqrt(2 gh)`
C. `(m)/(M + m) sqrt(2 gh)`
D. `(m)/(M) sqrt(2 gh)`

Answer

A

Explanation

`mv = (m + M)v_(1) rArr v_(1) = (mv)/(m + M)`
`v'^(2) = v_(1)^(2) - 2gh rArr 0 = v_(1)^(2) - 2gh`
`v_(1) = sqrt(2 gh)`
`(mv)/(m + M) = sqrt(2 gh)`
`v = (M + m)/(m) sqrt(2 gh)`