# Potential energy of certain spring when stretched through a distance of $x=10 J$. The amount of work that must be done on this spring to stretch it through an additional distance $x$ will be

$(a)\;30\;J \quad (b)\;20\;J \quad (c)\;10\;J \quad (d)\;40\;J$

Given P.E to stretch throgh 'x' is
$\large\frac{1}{2}$$k x^2=10\;J To stretch through additonal distance 'x' \large\frac{1}{2}$$k[(2s)^2-s^2]=3 \times \large\frac{1}{2}$$\times ks^2$
$\qquad=3 \times 10 J$
$\qquad=30\;J$
Hence a is the correct answer.
edited Jun 6, 2014