Question

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

• A. 2 U
• B. 25 U
• C. U/5
• D. 5 U

Answer 1

The correct option is A 2 U

Potential energy in a stretched spring is given by

$U=\frac{1}{2}K{x}^2$

$\frac{U_1}{U_2}={\left(\frac{x_1}{x_2}\right)}^2$

Given $X_1=2cm=0.2m,X_2=10cm=0.1m$

Substituting the values

$\frac{U_1}{U_2}={\left(\frac{0.02}{0.1}\right)}^2=={\left(\frac{1}{5}\right)}^2=\frac{1}{25}$

$U_2=25U_1=2U$