A $6 \,kg$ bomb at rest explodes into three equal pieces $P, Q$ and $R$. If $P$ flies with speed $30 \,m / s$ and $Q$ with speed $40 \,m / s$ making an angle $90^{\circ}$ with the direction of $P$. The angle between the direction of motion of $P$ and $R$ is about

A body at rest explodes into two pieces of unequal mass. The parts will move

An open water tight railway wagon of mass $5 \times 10^3 kg$ coasts at an initial velocity $1.2 m/s$ without friction on a railway track. Rain drops fall vertically downwards into the wagon. The velocity of the wagon after it has collected $10^3 kg$ of water will be ………….. $\mathrm{m}/ \mathrm{s}$

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 files off with $4 \,m s^{-1}$ speed, then its mass is ……… $kg$

A bullet of mass $5 \,g$ is shot from a gun of mass $5 \,kg$. The muzzle velocity of the bullet is $500\, m/s$. The recoil velocity of the gun is ……….. $m/s$