Question

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

• A. U/4
• B. 4U
• C. 8U
• D. 16U

Answer 1

Answer: (D)

Potential energy of a spring
$=\frac{1}{2}\times \text{ force constant }\times (\text{ extension }{)}^2$
$\therefore$ Potential energy $\propto (\text{ extension }{)}^2$.
or, $\frac{U_1}{U_2}={\left(\frac{x_1}{x_2}\right)}^2$
or, $\frac{U_1}{U_2}={\left(\frac{2}{8}\right)}^2$
or, $\frac{U_1}{U_2}=\frac{1}{16}$
or, $U_2=16U_1=16U$
$\left(\because U_1=U\right)$