The potential energy of a spring when stretched through a distance x is 10 J. What is the amount of work done on the same spring stretch it through an additional distance T?

Potential energy of the spring when stretched through a distance x.

$\mathrm{U}=\frac{1}{2}{\mathrm{kx}}^2=10\mathrm{J}$

When x becomes 2x, the potential energy will be

${\mathrm{U}}^{\mathrm{\prime }}=\frac{1}{2}\mathrm{k}(2\mathrm{x}{)}^2=4\times \frac{1}{2}{\mathrm{kx}}^2=4\times 10 = 40 \mathrm{J}$

$\therefore \text{ Work done }{\mathrm{U}}^{\mathrm{\prime }}-\mathrm{U}=40-10=30\mathrm{J}$