$A$ steel ball of radius $2 \, cm$ is at rest on a frictionless surface. Another steel ball of radius $4 \, cm$ moving at a velocity of $81 \, cm/s$ collides elastically with the first ball. After the collision,the smaller ball moves with a speed of ............. $cm/s$.

$A$ simple pendulum,made of a string of length $l$ and a bob of mass $m$,is released from a small angle $\theta_0$. It strikes a block of mass $M$,kept on a horizontal surface at its lowest point of oscillations,elastically. It bounces back and goes up to an angle $\theta_1$. Then $M$ is given by

$A$ particle of mass $m$ moving with velocity $u$ makes an elastic one-dimensional collision with a stationary particle of mass $m$. They are in contact for a very short time $T$. Their force of interaction increases from zero to $F_0$ linearly in time $T/2$, and decreases linearly to zero in further time $T/2$. The magnitude of $F_0$ is

When two particles collide elastically,then impulsive force can't change

$A$ moving particle collides with a stationary particle of mass $\frac{1}{n}$ times the mass of the moving particle. The fraction of its kinetic energy transferred to the stationary particle is:

Five identical elastic balls are suspended in a row with strings of equal length such that the distance between the sides of the balls is very small. If the ball at the right end is released from one side,then: