$A$ man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by $1 \, m/s$ and then has the same kinetic energy as the boy. The original speed of the man was
$\sqrt 2 \,m/s$
$( \sqrt 2 - 1)\,m/s$
$2\, m/s$
$(\sqrt 2 + 1)\, m/s$
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
The work done by a force $\vec F = (-6x^3\hat i)\, N$, in displacing a particle from $x = 4\, m$ to $x = -2\, m$ is .............. $\mathrm{J}$
In an elastic collision of two particles the following quantity is conserved
A particle of mass $m$ at rest is acted upon by a force $P$ for a time $t.$ Its kinetic energy after an interval $t$ is
Two identical particles are moving with same velocity $v$ as shown in figure. If the collision is completely inelastic then