$A$ body of mass $m$ moving with velocity $v$ undergoes a head-on elastic collision with another body of mass $2m$ which is initially at rest. The ratio of the kinetic energy $(K.E.)$ of the colliding body before and after the collision is: (in $: 1$)

$A$ body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2m$,which is 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

$A$ small particle elastically strikes a fixed smooth sphere of $4 \, cm$ radius,with a speed of $5 \, m/s$. The impact parameter for the collision is $2\sqrt{3} \, cm$. Calculate the angle of deflection of the particle ............... $^o$

$A$ ball $A$ of mass $m$ moving along the positive $x$-direction with kinetic energy $K$ and momentum $p$ undergoes an elastic head-on collision with a stationary ball $B$ of mass $M$. After the collision,the ball $A$ moves along the negative $x$-direction with kinetic energy $K/9$. The final momentum of $B$ is:

$A$ steel sphere of radius $1.2 \ cm$ collides with a second steel sphere at rest. If the collision is elastic and after the collision the first sphere continues to move in its initial direction with a velocity of $\frac{7}{9}$ times its initial velocity,then the radius of the second sphere is (in $cm$)

In an elastic collision of two billiard balls,which of the following quantities remain conserved during the short time of collision of the balls? (i.e.,when they are in contact)
$(a)$ Kinetic energy.
$(b)$ Total linear momentum.
Give reason for your answer in each case.