$A$ heavy body moving with a velocity of $6\,ms^{-1}$ collides elastically with a light body (whose mass is half of the mass of the heavy body) at rest. The velocity of the light body will be (in $ms^{-1}$):

$A$ body of mass $M$ moving at speed $V_{0}$ collides elastically with a mass $m$ at rest. After the collision,the two masses move at angles $\theta_{1}$ and $\theta_{2}$ with respect to the initial direction of motion of the body of mass $M$. The largest possible value of the ratio $M/m$,for which the angles $\theta_{1}$ and $\theta_{2}$ will be equal,is:

$A$ body of mass $m$ having an initial velocity $v$,makes a head-on collision with a stationary body of mass $M$. After the collision,the body of mass $m$ comes to rest and only the body having mass $M$ moves. This will happen only when:

$A$ body of mass $4\ kg$ collides head-on elastically with another body of mass $2\ kg$ kept at rest in free space. The time of collision is $0.02\ s$ and the average impulsive force acting on each body is $100\ N$. Find the velocity of the $2\ kg$ body after the impact. (in $m/s$)

$A$ ball moving with velocity $V$ undergoes a perfectly elastic collision with an identical ball moving in the opposite direction with velocity $2V$. Taking the direction of $V$ as positive,find the velocities of both balls after the collision.

$A$ sphere of mass $10 \ kg$ moving with a velocity of $10 \ m/s$ undergoes an elastic collision with a body of mass $5 \ kg$ moving in the same direction with a velocity of $4 \ m/s$. What are their velocities after the collision?