A ball of mass m moving at speed v collides with a massless spring of spring constant k mounted on a stationary box of mass M in free space. No mechanical energy is lost in the collision. If the system does not rotate, what is the maximum compression x of the spring?
Answer Choices
A. x=v \sqrt{\frac{m M}{(m+M) k}}
B. x=v \sqrt{\frac{m}{k}}
C. x=v \sqrt{\frac{M}{k}}
D. x=v \sqrt{\frac{m+M}{k}}
E. x=v \sqrt{\frac{(m+M)^{3}}{m M k}}