$A$ stationary particle explodes into two particles of masses $m_1$ and $m_2$ which move in opposite directions with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $E_1/E_2$ is:

$A$ spaceship of speed $v_0$ travelling along $+y$ axis suddenly shoots out one-fourth of its part with speed $2v_0$ along $+x$ axis. The $xy$ axes are fixed with respect to the ground. The velocity of the remaining part is:

$A$ man of mass $m$ is standing on a cart of mass $2m$. Initially, the cart is at rest. The man jumps horizontally with a relative velocity $u$ with respect to the cart. The work done by the internal forces of the man during the process of jumping will be:

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

Under the influence of mutual internal forces,which of the following is true for a system?

$A$ 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: