Two putty balls of equal mass moving with equal velocity in mutually perpendicular directions, stick together after collision. If the balls were initially moving with a velocity of $45\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$ each, the velocity of their combined mass after collision is

A moving body of mass $m$ and velocity $3 \mathrm{km} {\mathrm{h}}^{-1}$ collides with a body at rest and of mass $2m$ and then sticks to it. The velocity of the combined mass will be

A ball of mass $0.2 \mathrm{kg}$ rests on a vertical post of height $5 \mathrm{m}$. A bullet of mass $0.01 \mathrm{kg}$, travelling with a velocity $V \mathrm{m} {\mathrm{s}}^{-1}$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $20 \mathrm{m}$ and the bullet, at a distance of $100 \mathrm{m}$ from the foot of the post. The initial velocity $V$ of the bullet is

For the shown situation, if a collision between blocks $A$ and $B$ is perfectly elastic, then find the maximum energy (in $\mathrm{joules}$) stored in the spring.