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 stone tied to a string $L$ is whirled in a vertical circle, with the other end of the string at the centre. At a certain instant of time, the stone is as its lowest position and has a speed $u$. the magnitude of the change in its velocity as it reaches a position where the string is horizontal is

$ABCDE$ is a channel in the vertical plane, part $BCDE$ being circular with radius $r$ . A block is released from $A$ and slides without friction and without rolling. The block will complete the loop if $h$ is

The potential energy of a particle oscillating along $x-$ axis is given as $U =20+ (x – 2)^2$ where $U$ is in $joules$ and $x$ in $meters$ . Total mechanical energy of the particle is $36 \,J$. Maximum kinetic energy of the particle is …………… $\mathrm{J}$

A boy holds a uniform chain of length $2\,m$ which is kept on a smooth table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table ………….. $\mathrm{J}$