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?

The work done in joules in increasing the extension of a spring of stiffness $10\, N/cm$ from $4\, cm$ to $6\, cm$ is:

$A$ 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.

$A$ spring with spring constant $k$ is extended from $x = 0$ to $x = x_1$. The work done will be

Two springs with spring constants $K_1 = 1500 \, N/m$ and $K_2 = 3000 \, N/m$ are stretched by the same force. The ratio of potential energy stored in the springs will be

$A$ bungee jumper is jumping with the help of an elastic ideal rope (force constant $K$). The jumper steps off the bridge and falls from rest towards the river below. He does not hit the water. The mass of the jumper is $m$,and the natural length of the rope is $l$. Gravity is $g$. Assuming everything is ideal,choose the incorrect option.