Power applied to a particle varies with time as $P = [3t^2 -2t + 1]$ $watt$ then the change in kinetic energy of particle from $t = 2\,sec$ to $t = 4\,sec.$ ............... $\mathrm{J}$

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

A uniform chain of length $2\,m$ is kept on a table such that a length $60\,cm$ hangs freely from the edge of the table. The total mass of chain is $4\,kg$. The work done in pulling the entire chain on the table is ............. $\mathrm{J}$ (Take $g = 10\,m/s^2$)

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

$A$ particle of mass $m$ is released from $a$ height $H$ on $a$ smooth curved surface which ends into a vertical loop of radius $R$, as shown The minimum value of $H$ required so that the particle makes a complete vertical circle is given by

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 .............. $\mathrm{J}$