A body $A$ of mass $M$ while falling vertically downwards under gravity breaks into two parts; a body B of mass $1/3\,M$ and a body C of mass $2/3\,M$. The centre of mass of bodies B and C taken together shifts compared to that of body A towards
(1) depends on height of breaking
(2) does not shift
(3) body C
(4) body B

Two bodies $A$ and $B$ of mass $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_{0}$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision it is found that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_{0}$. The spring constant $k$ will be
(1) $m\frac{v_{0}^{2}}{x_{0}^{2}}$
(2) $m\frac{v_{0}}{2x_{0}}$
(3) $2m\frac{v_{0}}{x_{0}}$
(4) $\frac{2}{3}m\left(\frac{v_{0}}{x_{0}}\right)^{2}$