$A$ body of mass $5\; kg$ is moving with a momentum of $10\; kg\; m/s$. $A$ force of $0.2\; N$ acts on it in the direction of motion of the body for $10\; s$. Find the increase in its kinetic energy. (in $; J$)

In two separate collisions,the coefficients of restitution $e_1$ and $e_2$ are in the ratio $3: 1$. In the first collision,the relative velocity of approach is twice the relative velocity of separation. Then,the ratio between the relative velocity of approach and the relative velocity of separation in the second collision is:

$A$ ball of mass $m_1$ falls from height $h_1$ from rest to strike a spring of force constant $K$,which forces another ball of mass $m_2$ to jump on a horizontal floor at a height $h_2$ below it. Find the horizontal distance at which the ball of mass $m_2$ strikes the floor from the position of the start. [Assume the spring is fixed and the collision is elastic].

$A$ mass of $10 \, g$ moving with a velocity of $100 \, cm/s$ strikes a pendulum bob of mass $10 \, g$. The two masses stick together. The maximum height reached by the system now is ............... $cm$ $(g = 10 \, m/s^2)$.

Underline the correct alternative:
$(a)$ When a conservative force does positive work on a body,the potential energy of the body increases/decreases/remains unaltered.
$(b)$ Work done by a body against friction always results in a loss of its kinetic/potential energy.
$(c)$ The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system.
$(d)$ In an inelastic collision of two bodies,the quantities which do not change after the collision are the total kinetic energy/total linear momentum/total energy of the system of two bodies.

Which of the following graphs correctly represents the relationship between kinetic energy $(E)$,potential energy $(U)$,and height $(h)$ from the ground for a particle moving vertically?