$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/4$ remains stationary. The velocity of the other shell will be

An object of mass $3\,m$ at rest splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is

$A$ spacecraft of mass $M$ is moving in space with a velocity $v$. It explodes and breaks into two pieces. After the explosion,a piece of mass $m$ comes to rest. The velocity of the other piece is ......

$A$ man of mass $m_1$ is standing at a height $h$ from the floor in a gravity-free room. He throws a ball of mass $m_2$ downwards with a speed $u$. Find the distance of the man from the floor when the ball reaches the floor.

$A$ cannon shell fired breaks into two equal parts at its highest point. If one part retraces its path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$,then

$A$ projectile is fired with velocity $u$ at an angle $\theta$ with the horizontal. At the highest point of its trajectory,it splits into three segments of masses $m, m$,and $2m$. The first part falls vertically downward with zero initial velocity,and the second part returns via the same path to the point of projection. The velocity of the third part of mass $2m$ just after the explosion will be: