A small ball falling vertically downward with constant velocity $4m/s$ strikes elastically $a$ massive inclined cart moving with velocity $4m/s$ horizontally as shown. The velocity of the rebound of the ball is

A ball moving with a velocity of $6\, m/s$ strikes an identical stationary ball. After collision each ball moves at an angle of $30^o$ with the original line of motion. What are the speeds of the balls after the collision ?

A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at $x = 0$, its velocity at $x = 12\,m$ is .......... $m/s$

An object flying in alr with velocity $(20 \hat{\mathrm{i}}+25 \hat{\mathrm{j}}-12 \hat{\mathrm{k}})$ suddenly breaks in two pleces whose masses are in the ratio $1: 5 .$ The smaller mass flies off with a velocity $(100 \hat{\mathrm{i}}+35 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}) .$ The velocity of larger piece will be

A wire, which passes through the hole is a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$, the force it applies on the wire is

A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. The maximum height h attained by the particle is