Question

Two springs of force constants $1000N/m$ and $2000N/m$ are stretched by same force. The ratio of their respective potential energies is

• A. $2:1$
• B. $1:2$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is A $2:1$

$F=K_1{X}_1$
$F=K_2{X}_2$
$X_1=\frac{F}{1000}$

$X_2=\frac{F}{2000}$

$PE=\frac{1}{2}k{x}^2$

$P{E}_1=\frac{1}{2}{K}_1(x_1{)}^2$

$P{E}_1=\frac{1}{2}1000\times (\frac{F}{1000}{)}^2$

$P{E}_2=\frac{1}{2}2000\times (\frac{F}{2000}{)}^2$

$\frac{P{E}_1}{P{E}_2}=\frac{2}{1}$