In the figure shown, the two identical balls of mass $M$ and radius $R$ each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass $M$ and radius $R/2$, is coming down vertically and has a velocity $= v_0$ when it simultaneously hits the two balls and the smaller ball does not stop after collision, but continues to move downwards with $a$ speed $= v_0/2$, after the collision. Then, the speed of each bigger ball after collision is
$4v_0/ \sqrt 5 $
$2v_0/ \sqrt 5 $
$v_0 /2 \sqrt 5 $
None
A ball of mass $m$ strikes the inclined face of the wedge normally with speed $v_0$. The wedge is at rest on a rough horizontal surface before collision. The conservation of momentum is applicable for the event of collision for
$(i)$ $m$ as system, along $Y'$
$(ii) $ $M$ as system, along $Y'$
$(iii)$ $(M + m)$ as system, along $X$
$(iv)$ $(M + m)$ as system, along $Y$
Which of the following is correct?
A rod $AB$ is free to rotate in a vertical plane about a horizontal axis through $A$ as shown in figure. It is slightly disturbed from rest in its position of unstable equilibrium and when it is next vertical the end $B$ collides with a fixed peg and rebounds. If the rod comes to instantaneous rest when $AB$ is horizontal (as shown in figure) then :-
The quantity that is not conserved in an inelastic collision is
A ball moving with velocity $2 \,m/s$ collides head on with another stationary ball of double the mass. If the coefficient of restitution is $0.5,$ then their velocities after collision will be
Three different projectiles, each with the same mass, are fired with speed $v$ at a wall. In case $A,$ the projectile bounces straight back with speed $v.$ In case $B$, the projectile sticks to the wall. In case $C$, the projectile crashes through the wall and emerges with half its original speed. These three cases are shown here.
Place the impulse exerted by the wall on the projectile in each of these three cases in the correct order.