$A$ bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be

Two particles of equal mass $m$ have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+ \hat{j}}{2}\right)$. They collide completely inelastically. The energy lost in the process is

$A$ bullet of mass $m$ travelling with a speed $v$ hits a block of mass $M$ initially at rest and gets embedded in it. The combined system is free to move and there is no other force acting on the system. The heat generated in the process will be

$A$ bullet is fired from a gun. It hits a solid block resting on a frictionless surface,gets embedded into it,and both move jointly. In this process,

Ball $A$ of mass $1 \,kg$ moving along a straight line with a velocity of $4 \,ms^{-1}$ hits another ball $B$ of mass $3 \,kg$ which is at rest. After collision, they stick together and move with the same velocity along the same straight line. If the time of impact of the collision is $0.1 \,s$, then the force exerted on $B$ is (in $\,N$)

Two putty balls of equal mass $m$ moving with equal velocity $v = 45\sqrt{2} \, m/s$ in mutually perpendicular directions,stick together after collision. The velocity of their combined mass after collision is .................. $m/s$.