A rubber ball is released from a height of $5\, m$ above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take $g =10 ms ^{-2}$ ) (in $ms ^{-1}$)

In the figure shown, a small ball hits obliquely a smooth and horizontal surface with speed $u$ whose $x$ and $y$ components are indicated. If the coefficient of restitution is $\frac{1}{2}$, then its $x$ and $y$ components $v_x$ and $v_y$ just after collision are respectively

A body of mass $5\, kg$ moving with a velocity $10\,m/s$ collides with another body of the mass $20 \,kg$ at, rest and comes to rest. The velocity of the second body due to collision is ......... $m/s$

A molecule in a gas container hits a hortzontal wall with speed $200 \;m s ^{-1}$ and angle $30^{\circ}$ with the normal, and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?

$STATEMENT$-$1$ In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. because

$STATEMENT$-$2$ In an elastic collision, the linear momentum of the system is conserved.

A ball of mass $m$ is moving with a speed $V$ as shown in the figure. It undergoes inelastic collision with a ball of mass $2\ m$ which was initially at rest. The velocity of ball $2\ m$ after collision will be given by