$A$ gun fires a bullet of mass $50 \, g$ with a velocity of $30 \, m/s$. Because of this,the gun is pushed back with a velocity of $1 \, m/s$. The mass of the gun is .......... $kg$.

$A$ bomb at rest explodes into three pieces of equal masses. If two pieces move perpendicular to each other,each with a speed $v$,then the speed of the third piece is:

$A$ stationary particle explodes into two particles of masses $m_1$ and $m_2$ which move in opposite directions with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $E_1/E_2$ is:

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1 \, kg$ moves with a speed of $12 \, m s^{-1}$ and the second part of mass $2 \, kg$ moves with $8 \, m s^{-1}$ speed. If the third part flies off with $4 \, m s^{-1}$ speed,then its mass is ......... $kg$.

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

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 ............ $s$.