Question

When a long spring is stretched by $2cm$, its potential energy is $V$. If the spring is stretched by $10cm$, the potential energy in it will be:

• A. $10V$
• B. $25V$
• C. $\frac{V}{5}$
• D. $5V$

Answer 1

The correct option is B $25V$

Potential energy in a stretched spring is given by
$V=\frac{1}{2}k{x}^2$

$\therefore \frac{V_1}{V_2}={\left(\frac{x_1}{x_2}\right)}^2$

$\therefore \frac{V_1}{V_2}={\left(\frac{0.02}{0.1}\right)}^2$

$=\frac{1}{25}$

$V_2=25V_1=25V$