Work done on a certain spring when it is stretched to $1 \text{ mm}$ from its mean position is $10 \text{ J}$. The amount of work that must be done on the spring to stretch it further by $1 \text{ mm}$ is: (in $\text{ J}$)

$A$ spring has a natural length $l$ with one end fixed to the ceiling. The other end is fitted with a smooth ring which can slide on a horizontal rod fixed at distance $l$ below the ceiling. Initially,the spring makes an angle of $60^{\circ}$ with the vertical,when the system is released from rest. Find the angle of the spring with the vertical,when the velocity of the ring reaches half of the maximum velocity,which the ring can attain during the motion.

$A$ 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 of spring constant $5 \times 10^3 \, N/m$ is stretched initially by $5 \, cm$ from the unstretched position. Then the work required to stretch it further by another $5 \, cm$ is .............. $J$.

What is the work done by a spring force in a cyclic process?

When equal forces are applied to two springs with spring constants $1500 \, N/m$ and $3000 \, N/m$,what is the ratio of their stored potential energies?