$A$ bomb of $12 \, kg$ explodes into two pieces of masses $4 \, kg$ and $8 \, kg$. The velocity of the $8 \, kg$ mass is $6 \, m/s$. The kinetic energy of the other mass is ............. $J$.

$12 \,kg$ bomb at rest explodes into two pieces of $4 \,kg$ and $8 \,kg$. If the momentum of the $4 \,kg$ piece is $20 \,Ns$, what is the kinetic energy of the $8 \,kg$ piece (in $\,J$)?

$A$ ball of mass $m$ strikes the inclined face of the wedge of mass $M$ normally with speed $v_0$. The wedge is at rest on a rough horizontal surface before the collision. The conservation of momentum is applicable for the event of collision for:
$(i)$ $m$ as system,along $Y'$
$(ii)$ $M$ as system,along $Y'$
$(iii)$ $(M + m)$ as system,along $X$
$(iv)$ $(M + m)$ as system,along $Y$
Which of the following is correct?

$A$ buggy of mass $100\, kg$ is free to move on a frictionless horizontal track. Two men,each of mass $50\, kg$,are standing on the buggy,which is initially stationary. The men jump off the buggy with a velocity of $10\, m/s$ relative to the buggy. In one situation,the men jump one after the other. In another situation,the men jump simultaneously. What is the ratio of the recoil velocities of the buggy in the two cases?

$A$ shell,in flight,explodes into four unequal parts. Which of the following is conserved?

Newton's third law of motion leads to the law of conservation of