$A$ shell at rest on a smooth horizontal surface explodes into two fragments of masses $m_1$ and $m_2$. If just after explosion $m_1$ moves with speed $u$,then the work done by internal forces during the explosion is:

Explain why total linear momentum is conserved in an elastic collision,and define inelastic collision and perfectly inelastic collision.

$A$ bead of mass $m$ slides without friction on the wall of a vertical circular hoop of radius $R$ as shown in the figure. The bead moves under the combined action of gravity and a massless spring of constant $k$ attached to the bottom of the hoop. The natural (equilibrium) length of the spring is $R$. If the bead is released from the top of the hoop with negligible initial speed,what is the velocity of the bead when the length of the spring becomes $R$? ($g$ is the acceleration due to gravity)

$A$ rigid body of mass $4 \ kg$ initially at rest moves under the action of an applied horizontal force of $18 \ N$ on a table with a coefficient of kinetic friction of $0.2$. The work done by the applied force on the body in $10 \ s$ will be $.... \ J$.

$A$ body is moved from rest along a straight line by a machine delivering constant power. The ratio of displacement and velocity $(s/v)$ varies with time $t$ as :

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