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

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

State the law of conservation of total linear momentum for a system of particles.

$A$ bomb at rest explodes into three pieces of equal masses. If two pieces move perpendicular to each other,each with a speed $v$,then the speed of the third piece is:

An artillery piece of mass $M_1$ fires a shell of mass $M_2$ horizontally. Instantaneously after the firing,the ratio of kinetic energy of the artillery and that of the shell is:

If the resultant of all the external forces acting on a system of particles is zero,then from an inertial frame,one can surely say that