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

Answer

A

Explanation

By the conservation of linear momentum initial momentum of sphere =Final momentum of system
`mV=(m+M) v_(sys)....(i)`
if the system rises up to height h then by the conservation of energy
`1/2 (m+M)_(sys)^(2)=(m+M) gh`
`rArr v_(sys)=sqrt(2gh)`
Substituting this value in equation (i)
`V=((m+M)/m) sqrt(2gh)`