An athlete throws a shotput of mass $25 \,kg$ with an initial speed of $4 \,ms^{-1}$ at an angle of $45^{\circ}$ with the horizontal from a height of $2 \,m$ above the ground. Assuming air resistance to be negligible,the kinetic energy of the shotput when it just touches the ground is . . . . . . $\left(g=10 \,ms^{-2}\right)$ (in $\,J$)

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 simply lets go of the bag,which falls freely. Saina's backward swing then reaches maximum height $h_2$. Neglecting air resistance,how are the three heights related?

The mass of a person is $60 \, kg$. If he gains $10^5 \, \text{calories}$ of heat energy from food and the efficiency of his body is $28 \%$,then up to what height can he climb? (approximately) ($g = 9.8 \, m/s^2$,$J = 4.2 \, J/\text{cal}$)

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.

$A$ body $x$ with a momentum $p$ collides with another identical stationary body $y$ one-dimensionally. During the collision,$y$ gives an impulse $J$ to body $x$. Then,the coefficient of restitution is

In the figure shown,two identical balls of mass $M$ and radius $R$ each are placed in contact with each other on a frictionless horizontal surface. $A$ third ball of mass $M$ and radius $R$ is coming down vertically and has a velocity $v_0$ when it simultaneously hits the two balls and comes to rest. Then,each of the two bigger balls will move after the collision with a speed equal to: