Question

A long spring is stretched by $2\, cm$. Its potential energy is $U$. If the spring is stretched by $10\, cm$, the potential energy stored in it will be:

• A. $ \frac{U}{25} $
• B. $ \frac{U}{5} $
• C. $ 3\,U $
• D. $ 25\,U $

Answer 1

Answer: (D)

When a spring is stretched by $x \,cm$,
its stored potential energy is $U=\frac{1}{2} k x^{2}$
where $k$ is spring constant.
Given, $U_{1}=U, x_{1}=2\, cm , x_{2}=10 \,cm .$
$\therefore \frac{U_{1}}{U_{2}}=\frac{x_{1}^{2}}{x_{2}^{2}} $
$\Rightarrow \frac{U}{U_{2}}=\frac{(2)^{2}}{(10)^{2}}$
$\Rightarrow U_{2}=\frac{100}{4} U=25 \,U$
On stretching the spring further potential energy increases.