The potential energy of a long spring when stretched by 2 cm is $U$. If the spring is stretched by 8

Question

The potential energy of a long spring when stretched by 2 cm is $U$. If the spring is stretched by 8 cm , potential energy stored in it will be\

Professor PC Thomas Classes · Answer

(b) : Potential energy when spring is stretched by 2 cm is $U=\frac{1}{2} k x^{2}=\frac{1}{2} k(2)^{2}=2 k$\ Potential energy when spring is stretched by 8 cm is\ $U^{\prime}=\frac{1}{2} k(8)^{2}=32 k$\ From eqn (i) and (ii), we get\ $	herefore \quad \frac{U^{\prime}}{U}=\frac{32 k}{2 k}=16 \Rightarrow U^{\prime}=16 U$\