A bullet of mass $m$ strikes a block of mass $M$ connected to a light spring of stiffness $k$ , with a speed $V_0$ . If the bullet gets embedded in the block then, the maximum compression in the spring is

- A
${\left( {\frac{{{m^2}v_0^2}}{{(M + m)k}}} \right)^{1/2}}$

- B
${\left( {\frac{{Mmv_0^2}}{{2(M + m)k}}} \right)^{1/2}}$

- C
${\left( {\frac{{Mv_0^2}}{{2(M + m)k}}} \right)^{1/2}}$

- D
${\left( {\frac{{m{v^2}}}{{(M + m)k}}} \right)^{1/2}}$

Two identical balls $A$ and $B$ having velocities of $0.5\, m s^{-1}$ and $-0.3 \, m s^{-1}$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be

- [AIPMT 1994]

A sphere collides with another sphere of identical mass. After collision, the two spheres move. The collision is inelastic. Then the angle between the directions of the two spheres is

In the figure shown, a small ball hits obliquely a smooth and horizontal surface with speed $u$ whose $x$ and $y$ components are indicated. If the coefficient of restitution is $\frac{1}{2}$, then its $x$ and $y$ components $v_x$ and $v_y$ just after collision are respectively

A ball of mass $ m$ moving with velocity $V$, makes a head on elastic collision with a ball of the same mass moving with velocity $2V$ towards it. Taking direction of $V$ as positive velocities of the two balls after collision are

A ball of mass $10\, kg$ is moving with a velocity of $10\, m/s$. It strikes another ball of mass $5\, kg $ which is moving in the same direction with a velocity of $4 \,m/s$. If the collision is elastic, their velocities after the collision will be, respectively