$A$ bomb of mass $30 \, kg$ at rest explodes into two pieces of masses $18 \, kg$ and $12 \, kg$. The velocity of the $18 \, kg$ mass is $6 \, m/s$. The kinetic energy of the other mass is ....... $J$.

At a certain height,a body at rest explodes into two equal fragments with one fragment receiving a horizontal velocity of $10\sqrt{3} \text{ m/s}$. The horizontal distance between the two fragments,when their displacement vectors are inclined at $60^{\circ}$ relative to each other,is (take $g = 10 \text{ m/s}^2$):

At high altitude,a body at rest explodes into two equal fragments,with one fragment receiving a horizontal velocity of $10 \, m/s$. The time taken by the two radius vectors connecting the point of explosion to the fragments to make an angle of $90^o$ is ............ $s$.

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

$A$ bullet of mass $10\, g$ is fired from a gun of mass $1\, kg$. If the recoil velocity of the gun is $5\, m/s$,the muzzle velocity of the bullet is ........ $m/s$.

$A$ body is moving with a velocity $v$ and breaks up into two equal parts. One of the parts retraces its path with velocity $v$. Then the velocity of the other part is: