The potential energy of a long spring when stretched by 3 cm is $U$. If the spring is stretched by 1

Question

The potential energy of a long spring when stretched by 3 cm is $U$. If the spring is stretched by 12 cm, potential energy stored in it will be

Professor PC Thomas Classes · Answer

(b) : Potential energy when the spring is stretched by $x$ is $U = \frac{1}{2} k x^{2}$. Since $U \propto x^2$, when the extension increases from 3 cm to 12 cm (which is 4 times the initial extension), the new potential energy $U'$ becomes $4^2 = 16$ times the original. $	herefore U^{\prime} = 16 U$.