Question

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

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

Answer 1

Answer: (D)

When a spring is stretched by $xcm$,
its stored potential energy is $U=\frac{1}{2}k{x}^2$
where $k$ is spring constant.
Given, $U_1=U,x_1=2cm,x_2=10cm.$
$\therefore \frac{U_1}{U_2}=\frac{x_1^2}{x_2^2}$
$\Rightarrow \frac{U}{U_2}=\frac{(2{)}^2}{(10{)}^2}$
$\Rightarrow U_2=\frac{100}{4}U=25U$
On stretching the spring further potential energy increases.