$A$ body of mass $M$ is at rest. It explodes into three fragments. Two of the fragments,each of mass $M/4$,fly off perpendicular to each other with velocities of $3 \ m/s$ and $4 \ m/s$ respectively. What is the velocity of the third fragment in $m/s$?

$A$ 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:

Why is the law of conservation of linear momentum a universal and fundamental law?

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. The velocity of the man with respect to ground $v_1$ will be

$A$ body of mass $1 \,kg$, initially at rest, explodes and breaks into three parts. The masses of the parts are in the ratio $1: 1: 3$. The two pieces of equal mass fly off perpendicular to each other with a speed of $30 \,m/s$ each. The velocity of the heavier part in $m/s$ is