$A$ lead ball of mass $2 \ kg$ moving with a velocity of $1.5 \ ms^{-1}$ collides with a ball of mass $3 \ kg$ at rest. After the collision,the second ball moves with a velocity of $1 \ ms^{-1}$ in the original direction of motion of the first ball. Find $\Delta KE$ in $J$.

$A$ 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 (in $m/s$) after collision will be:

$A$ particle of mass $m_1$ moving along the $X$-axis collides with a stationary particle of mass $m_2$ and deviates by an angle $30^{\circ}$ to the $X$-axis as shown in the figure. If the percentage change in kinetic energy of the combined system of these two particles reduces by $50 \%$,then the ratio of the masses $\frac{m_2}{m_1}$ is

$A$ ball is allowed to fall freely from a height of $42 \ m$ from the ground. If the coefficient of restitution between the ball and the ground is $0.4$,then the total distance travelled by the ball before it comes to rest is (in $m$)

$A$ ball is projected vertically downward with an initial velocity from a height of $20 \ m$ onto a horizontal floor. During the impact,it loses $50\%$ of its energy and rebounds to the same height. The initial velocity of its projection is ............ $m/s$.

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