$A$ ball of mass $100 \, g$ is dropped from a height $h = 10 \, cm$ onto a platform fixed at the top of a vertical spring (as shown in the figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$. The spring constant is .......... $N \, m^{-1}$. (Use $g = 10 \, m \, s^{-2}$)

$A$ spring with force constant $k$ is initially stretched by a distance $x$. If it is further stretched by a distance $y$,the work done during the second stretching is.........

An elastic spring of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. Work done during the second stretching is

$A$ body of mass $0.5 \ kg$ moves with a speed of $1.5 \ m/s$ on a smooth horizontal surface. It hits a massless spring with a force constant $k = 50 \ N/m$. What will be the maximum compression of the spring in $m$?

One end of a spring of spring constant $80 \ Nm^{-1}$ and unstretched length of $30 \ cm$ is fixed at point $A$ and the other end of the spring is fitted with a smooth ring of mass $300 \ g$ as shown in the figure. The ring is allowed to slide on a horizontal rod fixed at a height of $40 \ cm$. Initially the spring makes an angle of $60^{\circ}$ with the vertical and the system of spring and ring is released from rest. The speed of the ring when the spring becomes vertical is . . . . . . $ms^{-1}$.

If the potential energy of a spring is $V$ on stretching it by $2 \, cm$,then its potential energy when it is stretched by $10 \, cm$ will be