Two springs have their force constants as $k_1$ and $k_2$ $(k_1 > k_2)$. When they are stretched by the same force,which of the following is true?

$A$ ring of mass $m$ is attached to a horizontal spring of spring constant $k$ and natural length $l_0$. The other end of the spring is fixed,and the ring can slide on a smooth horizontal rod as shown. Now,the ring is shifted to position $B$ and released. The speed of the ring when the spring attains its natural length is:

$A$ 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 $g = 10 \, m \, s^{-2}$)

Two springs with spring constants $1500 \ N/m$ and $3000 \ N/m$ respectively are stretched by the same force. What is the ratio of their potential energies?

When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law,the spring stretches by $2\, cm$. The work required to be done by an external agent in stretching this spring by $5\, cm$ will be ......... $J$ $(g = 9.8\, m/s^2)$.

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 . . . . . . $ms^{-1}$.