Two wooden blocks of mass $M_1$ and $M_2$ rest on a frictionless table. $A$ bullet of mass $m$ is fired at $M_1$ with speed $v$,which gets embedded in it,and the two together finally collide with $M_2$. Find the velocity of $M_2$ after the collision. (Assume the collision between the $(M_1+m)$ system and $M_2$ is elastic and treat the problem as one-dimensional.)

$A$ body of mass $(4m)$ is lying in the $x-y$ plane at rest. It suddenly explodes into three pieces. Two pieces,each of mass $(m)$,move perpendicular to each other with equal speeds $(v)$. The total kinetic energy generated due to the explosion is ................. $mv^2$.

In the case of circular motion of a body,if a tangential force also acts on the body in addition to a centripetal force,then the work done:

Calculate the work done to pull a block of mass $M$ by a constant force $F$ as shown in the figure. The coefficient of friction between the block and the ground is $\mu$.

$A$ ball of mass $10\, kg$ moving with a velocity $10 \sqrt{3} \, m/s$ along the $x$-axis,hits another ball of mass $20\, kg$ which is at rest. After the collision,the first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along the $y$-axis with a speed of $10 \, m/s$. The second piece starts moving at an angle of $30^{\circ}$ with respect to the $x$-axis. The velocity of the ball moving at $30^{\circ}$ with the $x$-axis is $x \, m/s$. The configuration of pieces after the collision is shown in the figure. The value of $x$ to the nearest integer is:

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
According to the observer $A$: