A $15\, g$ ball is shot from a spring gun whose spring has a force constant of $600\, N\, m$. The spring is compressed by $3\, cm$. The greatest possible velocity of the ball for this compression is ............. $\mathrm{m}/ \mathrm{s}$   $(g = 10\, m/s^2$)

A bag of sand of mass $M$ is suspended by a string. A bullet of mass $m$ is fired at it with velocity $v$ and gets embedded into it. The loss of kinetic energy in this process is

A particle moves along the $x-$ axis from $x = 0$ to $x = 5\,m$ under the influence of a force $F$ (in $N$ ) given by $F = 3x^2 -2x + 7$ . Calculate the work done by this force .............. $\mathrm{J}$

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by

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

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:-