A bomb, initially at rest, explodes into several pieces.

(a) Is linear momentum of the system conserved? 

(b) Is kinetic energy of the system conserved? Explain.

You are standing perfectly still and then you take a step forward. Before the step your momentum was zero, but afterward you have some momentum. Is the principle of conservation of momentum violated in this case?

Discuss the possibility of conservation of linear momentum of a block moving on a rough inclined plane if $\mu =\tan \theta .$

A mud ball at rest explodes into three fragments of masses in the ratio $1: 2: 1.$ The two equal masses move with velocities $2\hat{i}+5\hat{j}-6\hat{k}$ and $-4\hat{i}+3\hat{j}+2\hat{k}.$ Find the velocity of the third mass.

(a) A rail road car of mass $M$ is moving without friction on a straight horizontal track with a velocity $u.$ A man of mass $\mathrm{m}$ lands on it normally from a helicopter. What will be the new velocity of the car?

(b) If now the man begins to run on it with speed $v_{\text{rel }}$ with respect to car in a direction opposite to motion of the car, what will be the new velocity of the car?

Two identical buggies $1$ and $2$ with one man in each move along parallel rails. When the buggies are opposite to each other, the men jump in a direction perpendicular to the direction of motion of buggies, so as to exchange their places. As a consequence, buggy $1$ stops and buggy $2$ keeps moving in the same direction with its final velocity $v.$ Find the initial velocities $v_1$ and $v_2$ of buggies. Mass of each buggy (without man) equals $M,$ mass of each man is $m;$ ignore frictional effects anywhere and the buggies are constrained to move along the rails only.