$A$ body of mass $5\,kg$ is moving with a momentum of $10\,kg\,m/s$. Now a force of $2\,N$ acts on the body in the direction of its motion for $5\,s$. The increase in the kinetic energy of the body is $...........J$.

$A$ person trying to lose weight by burning fat lifts a mass of $10 \ kg$ up to a height of $1 \ m$, $1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times 10^7 \ J$ of energy per $kg$, which is converted to mechanical energy with a $20\%$ efficiency rate. Take $g = 9.8 \ m/s^2$.

State if each of the following statements is true or false. Give reasons for your answer.
$(a)$ In an elastic collision of two bodies,the momentum and energy of each body is conserved.
$(b)$ Total energy of a system is always conserved,no matter what internal and external forces on the body are present.
$(c)$ Work done in the motion of a body over a closed loop is zero for every force in nature.
$(d)$ In an inelastic collision,the final kinetic energy is always less than the initial kinetic energy of the system.

Assertion $(A)$: When we bounce a ball on the ground, it comes to rest after a few bounces, losing all its energy. This is an example of violation of conservation of energy.
Reason $(R)$: Energy can change from one form to another but the total energy is always conserved.
Which of the following is true?

$A$ ball is dropped vertically downwards from a height $h$ above the ground. It hits the ground inelastically and bounces up vertically. Neglecting subsequent motion and air resistance,which of the following graphs represents the variation between speed $(v)$ and height $(h)$ correctly?

$A$ block moving horizontally on a smooth surface with a speed of $40 \, m/s$ splits into two equal parts. If one of the parts moves at $60 \, m/s$ in the same direction,then the fractional change in the kinetic energy will be $x: 4$ where $x = ..... .$