Two identical balls of mass $2 \ kg$ are moving towards each other with a velocity of $5 \ m/s$. They collide and come to rest after the collision. What is the work done by the internal forces in $J$?

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 $J$)

Particle $A$ of mass $m_{1}$ moving with velocity $(\sqrt{3} \hat{i} + \hat{j}) \, m/s$ collides with another particle $B$ of mass $m_{2}$ which is at rest initially. Let $\vec{V}_{1}$ and $\vec{V}_{2}$ be the velocities of particles $A$ and $B$ after collision,respectively. If $m_{1} = 2m_{2}$ and after collision $\vec{V}_{1} = (\hat{i} + \sqrt{3} \hat{j}) \, m/s$,the angle between $\vec{V}_{1}$ and $\vec{V}_{2}$ is $......^{\circ}$.

$A$ body moving with velocity $v$ has momentum and kinetic energy numerically equal. What is the value of $v$ in $m/s$?

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is $1.5 \; m$,what is the speed (in $m/s$) with which the bob arrives at the lowermost point,given that it dissipated $5 \%$ of its initial energy against air resistance?

$A$ motor drives a body along a straight line with a constant force. The power $P$ developed by the motor must vary with time $t$ according to