A particle falls from a height $h $ upon a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution, the total distance travelled before rebounding has stopped is
$h\left( {\frac{{1 + {e^2}}}{{1 - {e^2}}}} \right)$
$h\left( {\frac{{1 - {e^2}}}{{1 + {e^2}}}} \right)$
$\frac{h}{2}\left( {\frac{{1 - {e^2}}}{{1 + {e^2}}}} \right)$
$\frac{h}{2}\left( {\frac{{1 + {e^2}}}{{1 - {e^2}}}} \right)$
A ball of mass $ m$ moving with velocity $V$, makes a head on elastic collision with a ball of the same mass moving with velocity $2V$ towards it. Taking direction of $V$ as positive velocities of the two balls after collision are
In $a$ one dimensional collision between two identical particles $A$ and $B, B$ is stationary and $A$ has momentum $p$ before impact. During impact, $B$ gives impulse $J$ to $A.$
A rubber ball is dropped from a height of $5 \,m$ on a planet where the acceleration due to gravity is not known. On bouncing, it rises to $1.8\, m$. The ball loses its velocity on bouncing by a factor of
$Assertion$ : In an elastic collision of two billiard balls, the total kinetic energy is conserved during the short time of oscillation of the balls (i.e., when they are in contact).
$Reason$ : Energy spent against friction does not follow the law of conservation of energy.
A bullet when fired at a target with a velocity of $100\,\,m/sec$ penetrates one metre into it. If the bullet is fired at a similar target with a thickness $0.5\,\,metre,$ then it will emerge from it with a velocity of