$A$ shell of mass $200\, g$ is ejected from a gun of mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $m/s$.

$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/3$ remains stationary. The velocity of the other part will be

$A$ 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:

$A$ man of mass $100\,kg$ is standing on a platform of mass $200\,kg$ which is kept on a smooth ice surface. If the man starts moving on the platform with a speed $30\,m/s$ relative to the platform,then calculate with what velocity relative to the ice the platform will recoil.

$A$ body of mass $50 \, kg$ is projected vertically upwards with a velocity of $100 \, m/s$. After $5 \, s$,the body breaks into two pieces of mass $20 \, kg$ and $30 \, kg$. If the $20 \, kg$ piece travels upwards with a velocity of $150 \, m/s$,what is the velocity of the $30 \, kg$ block?

$A$ shell of mass $20 \,kg$ at rest explodes into two fragments whose masses are in the ratio $2 : 3$. The smaller fragment moves with a velocity of $6 \,ms^{-1}$. The kinetic energy of the larger fragment is (in $\,J$)