$A$ shell of mass $M$ initially at rest suddenly explodes into three fragments. Two of these fragments are of mass $M/4$ each, which move with velocities $3 \text{ m/s}$ and $4 \text{ m/s}$ respectively in mutually perpendicular directions. The magnitude of the velocity of the third fragment is: (in $\text{ m/s}$)

$A$ 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

$A$ body of mass $M$ at rest explodes into three pieces,in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \, m/s$ and $40 \, m/s$ respectively. The velocity of the third piece will be ............... $\, m/s$.

In an explosion,a body breaks up into two pieces of unequal masses. In this process:

$A$ mass $M$ moving with velocity $V$ along $X$-axis collides and sticks to another mass $2M$ which is moving along $Y$-axis with velocity $3V$. The velocity of the combination, after the collision is

An object of mass $2m$ is projected with a speed of $100 \ m/s$ at an angle $\theta = \sin^{-1}(3/5)$ to the horizontal. At the highest point, the object breaks into two pieces of same mass $m$ and the first one comes to rest. The distance between the point of projection and the point of landing of the second piece (in metres) is $(g = 10 \ m/s^2)$.