Question

A long spring, when stretched by a distance $ x, $ has potential energy $U$. On increasing the stretching to $ nx, $ the potential energy of the spring will be

• A. $ \frac{U}{n} $
• B. $ nU $
• C. $ {{n}^{2}}U $
• D. $ \frac{U}{{{n}^{2}}} $

Answer 1

Answer: (C)

Potential energy of the spring
$ U=\frac{1}{2}k{{x}^{2}} $ ...(i)
and $ U'=\frac{1}{2}k{{(nx)}^{2}} $
$ \Rightarrow $ $ U'={{n}^{2}}\frac{1}{2}k\,x $
$ \therefore $ $ U'={{n}^{2}}U $ [From Eq. (i)]