Write the law of conservation of total linear momentum for the system of particle.

A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. The maximum height h attained by the particle is 

A balloon filled with helium rises against gravity increasing its potential energy. The speed of the balloon also increases as it rises. How do you reconcile this with the law of conservation of mechanical energy ? You can neglect viscous drag of air and assume that density of air is constant.

Starting from rest on her swing at initial height $h_0$ above the ground, Saina swings forward. At the lowest point of her motion, she grabs her bag that lies on the ground. Saina continues swinging forward to reach maximum height $h_1$ . She then swings backward and when reaching the lowest point of motion again, she simple lets go off the bag, which falls freely. Saina's backward swing then reaches maximum height $h_2$ . Neglecting air resistance, how are the three heights related?

A bomb at rest explodes into three fragments $X, Y$ and $Z$. Each one of them has the same mass. Which of the following correctly describes the motion of the fragments?

A space craft of mass $M$ is moving with velocity $V$ and suddenly explodes into two pieces. A part of it of mass m becomes at rest, then the velocity of other part will be