A block of mass M lying on a smooth· horizontal surface is rigidly attached ·to a light horizontal ·spring of spring constant k. The other end of the spring is rigidly connected to a fixed wall. A stationary gun fires ·bullets of mass m each in horizontal direction with speed `upsilon_(0)` one after other. The bullets hit the block and get embedded to it. The first bullet hits the block at t=0, the second bullent hits at `t=2pisqrt((M+m)/(k))+2pisqrt((M+2m)/(k))` and so on. The maximum comression in the spring after the `n^(th)` bullet hits is :

Options

A. `(nm upsilon_(0)sqrt(k))/((M+nm)^(3//2))`
B. `((M+nm)^(3//2))/(nm upsilon_(0)sqrt(k))`
C. `(sqrt(nm upsilon_(0)k))/((M+nm)^(3//2))`
D. `(nm upsilon_(0))/(sqrt(k(M+nm)))`

Answer

D