When a long spring of $4 \ cm$ is stretched by $1 \ cm$,the potential energy stored in the spring is $U$. If it is stretched by $4 \ cm$,the potential energy stored in it is (in $U$)

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 ................ $J$.

$A$ block of mass $m$ is hung vertically from an elastic thread of force constant $\frac{2mg}{a}$. Initially,the thread is at its natural length and the block is allowed to fall freely. The work done on the block by the Earth when it passes through the equilibrium position will be:

If a spring is stretched by a force $T$,what is the potential energy stored in the spring? (Given $T$ is the tension/force and $k$ is the spring constant.)

$A$ block of mass $m$ is pushed against a spring with spring constant $k$ which is attached to a wall. The block slides on a frictionless table as shown in the figure. The natural length of the spring is $\ell_0$ and it is compressed to half of its natural length when the block is released. What will be the final velocity of the block?

Two springs have spring constants $k_{A}$ and $k_{B}$ such that $k_{A} > k_{B}$. If both springs are stretched by the same extension $x$,the work required will be: