A particle fall from height $h$ on $a$ static horizontal plane rebounds. If $e$ is coefficient of restitution then before coming to rest the total distance travelled during rebounds will be:-
$h\left( {\frac{{1 + {e^2}}}{{1 - {e^2}}}} \right)$
$h\left( {\frac{{1 - {e^2}}}{{1 + {e^2}}}} \right)$
$\frac{h}{2}\left( {\frac{{1 - {e^2}}}{{1 + {e^2}}}} \right)$
$\frac{h}{2}\left( {\frac{{1 + {e^2}}}{{1 - {e^2}}}} \right)$
A ball of mass $M$ falls from a height $h$ on a floor which the coefficient of restitution is $e$. The height attained by the ball after two rebounds is
A ball of mass $M$ falls from a height $h$ on a floor. If co-efficient of restitution is $e$, the height attained by the ball after two rebounds is
A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, work required to pull the hanging part on to the table is
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.
Consider two carts, of masses $m$ and $2m$ , at rest on an air track. If you push both the carts for $3\,s$ exerting equal force on each, the kinetic energy of the light cart is