A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2: 2: 1$. If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$, the speed of the third (lighter) fragment is :

A cart loaded with sand moving with velocity $v$. Sand is falling through the hole as shown in diagram then after falling on the ground sand 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 files off with $4 \,m s^{-1}$ speed, then its mass is ……… $kg$

A shell at rest at the origin explodes into three fragments of masses $1\ kg$ , $2\ kg$ and $m\ kg$ . The $1\ kg$ and $2\ kg$ pieces fly off with speeds of $5\ ms^{-1}$ along $x-axis$ and $6\ ms^{-1}$ along $y-axis$ respectively. If the $m\, kg$ piece flies off with a speed of $6.5\ ms^{-1}$ , the total mass of the shell must be    ……… $kg$

A bullet $10\,g$ leaves the barrel of gun with a velocity of $600\,m / s$. If the barrel of gun is $50\,cm$ long and mass of gun is $3\,kg$, then value of impulse supplied to the gun will be $…..\,Ns$