A ball of mass `m` is projected with a speed `v` into the barrel of a spring gun of mass `M` initially at rest lying on a frictionless surface. The mass sticks in the barrel at the point of maximum compression in the spring. The fraction of kinetic energy of the ball stored in the spring is

Options

A. `m/M`
B. `M/(m+M)`
C. `m/(M+M)`
D. none of these

Answer

B

Explanation

At maximum compression when `m` sticks to `M`,
`mv=(M+m)V`
` V=(mv)/(M+m)`
Fraction of `KE` stored in spring `f=(K_(i)-K_(f))/K_(i)`
`:. F=1-(1/2(M+m)V^(2))/(1/2mv^(2))impliesf=1(m/(M+m))=M/(M+m)`