$A$ spring with spring constant $k$ when stretched through $1 \, cm$,the potential energy is $U$. If it is stretched by $4 \, cm$,the potential energy will be (in $U$)

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

$A$ spring,when stretched by $2 \,mm$,has a potential energy of $4 \,J$. If it is stretched by $10 \,mm$,its potential energy will be:

If a spring extends by $x$ on loading,then the energy stored by the spring is (if $T$ is tension in the spring and $k$ is spring constant).

$A$ ball of mass $m$ falls from a height $h$ onto a platform attached to a vertical spring. The platform is displaced by a distance $x$. What is the spring constant?

$A$ ball of mass $4\, kg$,moving with a velocity of $10\, ms^{-1}$,collides with a spring of length $8\, m$ and force constant $100\, Nm^{-1}$. The length of the compressed spring is $x\, m$. The value of $x$,to the nearest integer,is ........ .