A ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending  down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $\mathrm{m}/ \mathrm{s}$

A mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass initially at rest. After collision the first mass moves with velocity $\frac{v}{\sqrt 3}$ in a  direction perpendicular to its initial direction of motion. The speed of second mass after collision is 

If the momentum of a body increases by $0.01\%$, its kinetic energy will increase by ........... $\%$

A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be

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 of mass ${M_1}$ collides elastically with another mass ${M_2}$ at rest. There is maximum transfer of energy when