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 block of mass $1\,kg$ is pushed up a surface inclined to horizontal at an angle of $30^o$ by a force of $10\,N$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1$. If the block is pushed up by $10\,m$  along the inclined calculate 

$(a)$ work done against gravity

$(b)$ work done against force of friction

$(c)$ increases in potential energy

$(d)$ increases in kinetic energy

$(e)$ work done by applied force

A disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v$, the height to which the disc will rise will be

A uniform chain of length $2\,m$ is kept on a table such that a length $60\,cm$ hangs freely from the edge of the table. The total mass of chain is $4\,kg$. The work done in pulling the entire chain on the table is …………. $\mathrm{J}$ (Take $g = 10\,m/s^2$)

The potential energy of a diatomic molecule is given by $U = \frac{A}{{{r^{12}}}} – \frac{B}{{{r^6}}}$ . $A$ and $B$ are positive constants. The distance $r$ between them at equilibrium is