$A$ 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 ............. $kJ$.

$A$ girl riding a bicycle along a straight road with a speed of $5 \, m/s$ throws a stone of mass $0.5 \, kg$ which has a speed of $15 \, m/s$ with respect to the ground along her direction of motion. The mass of the girl and bicycle is $50 \, kg$. Does the speed of the bicycle change after the stone is thrown? What is the change in speed,if so?

$A$ shell of mass $5 M$, acted upon by no external force and initially at rest, bursts into three fragments of masses $M, 2 M$, and $2 M$ respectively. The first two fragments move in opposite directions with velocities of magnitudes $2 v$ and $v$ respectively. The third fragment will

$A$ cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is:

$A$ body at rest breaks into three fragments. Two fragments of equal mass fly off perpendicular to each other with a speed of $30 \; m/s$. The mass of the third fragment is three times that of the other two fragments. What will be the direction and magnitude of the velocity of the third fragment immediately after the explosion?