Three objects $A$,$B$,and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m$,$2m$,and $m$,respectively. The object $A$ moves towards $B$ with a speed of $9 \ m/s$ and makes an elastic collision with it. Thereafter,$B$ makes a completely inelastic collision with $C$. All motions occur on the same straight line. Find the final speed (in $m/s$) of the object $C$.

$A$ particle of mass $m$ is dropped from a height $h$ above the ground. At the same time,another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$. If they collide head-on completely inelastically,the time taken for the combined mass to reach the ground,in units of $\sqrt{\frac{h}{g}}$,is

Two massless strings of length $5\, m$ hang from the ceiling very near to each other as shown in the figure. Two balls $A$ and $B$ of masses $0.25\, kg$ and $0.5\, kg$ are attached to the strings. The ball $A$ is released from rest at a height of $0.45\, m$ as shown in the figure. The collision between the two balls is completely elastic. Immediately after the collision,the kinetic energy of ball $B$ is $1\, J$. The velocity of ball $A$ just after the collision is

$A$ ball loses $15.0\%$ of its kinetic energy when it bounces back from a concrete wall. With what speed must you throw it vertically down from a height of $12.4\, m$ to have it bounce back to the same height (ignore air resistance)? ............. $m / s$

In a one-dimensional collision between two identical particles $A$ and $B$, $B$ is stationary and $A$ has momentum $p$ before impact. During impact, $B$ gives impulse $J$ to $A$.

The linear momentum of a body of mass $8 \ kg$ is $24 \ kg \ m \ s^{-1}$. If a constant force of $24 \ N$ acts on the body in the direction of motion of the body for a time of $3 \ s$,then the increase in the kinetic energy of the body is (in $J$)