$A$ bomb of mass $16 \ kg$ at rest explodes into two pieces of masses $4 \ kg$ and $12 \ kg.$ The velocity of the $12 \ kg$ mass is $4 \ m s^{-1}.$ The kinetic energy of the other mass is .............. $J$.

$A$ body of mass $M$ at rest explodes into three pieces,in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \, m/s$ and $40 \, m/s$ respectively. The velocity of the third piece will be ............... $\, m/s$.

$A$ bullet is fired from a rifle. If the rifle recoils freely,then the kinetic energy of the rifle is

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When the person standing at $A$ jumps from the trolley towards the left with $u_{rel}$ with respect to the trolley,then:

Three masses $m$,$2m$,and $3m$ are moving in the $x-y$ plane with speeds $3u$,$2u$,and $u$ respectively,as shown in the figure. The three masses collide at the same point $P$ and stick together. The velocity of the resulting mass will be

$A$ body initially at rest breaks up into two pieces of masses $2 M$ and $3 M$ respectively,together having a total kinetic energy $E$. The piece of mass $2 M$,after breaking up,has a kinetic energy: