$A$ bomb of mass $3.0 \, kg$ explodes in air into two pieces of masses $2.0 \, kg$ and $1.0 \, kg$. The smaller mass travels at a speed of $80 \, m/s$. The total energy imparted to the two fragments is ............. $kJ$.

$A$ particle of mass $4m$ explodes into three pieces of masses $m, m$ and $2m$. The equal masses move along the $X$-axis and $Y$-axis with velocities $4 \text{ ms}^{-1}$ and $6 \text{ ms}^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

Two balls in free space are colliding with each other. Which of the following statements regarding linear momentum conservation of the system is true?

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

$A$ 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?

$A$ bullet of mass $50 \, g$ is fired from a $5 \, kg$ gun with a velocity of $1 \, km/s$. The speed of recoil of the gun is .......... $m/s$.