The $P.E.$ of a certain spring when stretched from natural length through a distance $0.3\, m$ is $10\, J$. The amount of work in joule that must be done on this spring to stretch it through an additional distance $0.15\, m$ will be ................ $J$.

$A$ spring of force constant $k$ is cut into two parts at one-third of its length. When both parts are stretched by the same amount,the work done in the two parts will be:

$A$ light elastic spring is placed on a massless platform as shown in the figure. $A$ sand particle of mass $0.1 \ kg$ is dropped onto the spring platform from a height of $0.24 \ m$. The particle sticks to the platform,causing the spring to compress by $0.01 \ m$. From what height should the particle be dropped so that the spring is compressed by $0.04 \ m$ (in $m$)?

The potential energy of a long spring when stretched by $2\,cm$ is $U$. If the spring is stretched by $8\,cm$,the potential energy stored in it will be $.......\,U$.

$A$ 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.

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