A ball of mass $m$ is dropped from a heigh $h$ on a platform fixed at the top of a vertical spring, as shown in figure. The platform is depressed by a distance $x.$ Then the spring constant is
$\frac{{mg}}{{(h + x)}}$
$\frac{{mg}}{{(h + 2x)}}$
$\frac{{2mg(h + x)}}{{{x^2}}}$
$\frac{{mg}}{{(2h + x)}}$
When a ball is freely fallen from a given height it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce ?
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 particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as, $a_c = k^2rt^2$, The power delivered to the particle by the forces acting on it is
Two bodies of masses $m_1$ and $m_2$ are moving with same kinetic energy. If $P_1$ and $P_2$ are their respective momentum, the ratio $\frac{P_1}{P_2}$ is equal to
A particle moves under the effect of a force $F = cx$ from $x = 0$ to $x = x_1$. The work done in the process is