$A$ 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 ............. $cm/s$.

$A$ smooth sphere $A$ of mass $m$ collides elastically with an identical sphere $B$ at rest. The velocity of $A$ before collision is $8 \ m/s$ in a direction making $60^{\circ}$ with the line of centers at the time of impact.
$(i)$ The sphere $A$ comes to rest after collision.
$(ii)$ The sphere $B$ will move with a speed of $8 \ m/s$ after collision.
$(iii)$ The directions of motion of $A$ and $B$ after collision are at right angles.
$(iv)$ The speed of $B$ after collision is $4 \ m/s$.
The correct option is:

$A$ ball of mass $1 \ kg$ moving along the $X$-direction collides elastically with a stationary ball of mass $m$. The first ball (mass $= 1 \ kg$) recoils at a right angle to its original direction of motion. If the second ball starts moving at an angle $30^{\circ}$ with the $X$-axis,the value of $m$ must be (in $kg$)

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with an angular velocity $\omega$ and its center of mass is moving with a linear velocity $v$. It undergoes an elastic collision with a stationary sphere $B$. (Ignore friction everywhere). If the angular speeds after the collision are $\omega_A$ and $\omega_B$ respectively,then:

$A$ point mass $M$ moving with a certain velocity collides with a stationary point mass $M / 2$. The collision is elastic and in one-dimension. Let the ratio of the final velocities of $M$ and $M / 2$ be $x$. The value of $x$ is

Which of the following is not a perfectly inelastic collision?