A particle of mass m moving with horizontal speed $6\, m/sec$ as shown in figure. If $m < < M$ then for one dimensional elastic collision, the speed of lighter particle after collision will be

Two masses of $0.25\, kg$ each moves towards each other with speed $3\, ms^{-1}$ and $1\, ms^{-1}$. Then they collide and stick together. Find the final velocity .............. $\mathrm{m} \mathrm{s}^{-1}$

A body of mass $1\,kg$ collides head on elastically with a stationary body of mass $3\,kg$. After collision, the smaller body reverses its direction of motion and moves with a speed of $2\,m / s$. The initial speed of the smaller body before collision is $..........ms ^{-1}$

A ball moving with velocity $2 \,m/s$ collides head on with another stationary ball of double the mass. If the coefficient of restitution is $0.5,$ then their velocities after collision will be

A body $x$ with a momentum $p$ collides with another identical stationary body $y$ one dimensionally. During the collision $y$ gives an impulse $J$ to body $x$. Then coefficient of restitution is

Body $A$ of mass $4 \;\mathrm{m}$ moung with speed $u$ collides with another body $B$ of mass $2\; \mathrm{m}$, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body $A$ is