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 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
In the non-relativistic regime, if the momentum, is increased by $100\%$, the percentage increase in kinetic energy is
A body moving with speed $v$ in space explodes into two piece of masses in the ratio $1 : 3.$ If the smaller piece comes to rest, the speed of the other piece is
A body is dropped from a height $h$ . If it acquires a momentum $p$ just before striking the ground, then the mass of the body is
Two blocks $A$ and $B$ of masses $1\, kg$ and $2\, kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to strech the spring and then released. The ratio of $K.E.s$ of both the blocks is