Question

The ratio of spring constants of two springs is $2:3$. What is the ratio of their potential energy, if they are stretched by the same force?

• A. $2:3$
• B. $3:2$
• C. $4:9$
• D. $9:4$

Answer 1

Answer: (B)

The spring forces are
$\because F=k_1{x}_1$ and $F=k_2{x}_2$
$\therefore k_1{x}_1=k_2{x}_2$
$\Rightarrow \frac{k_1}{k_2}=\frac{x_2}{x_1}$
$\Rightarrow \frac{(PE{)}_1}{(PE{)}_2}=\frac{k_1{x}_1^2}{k_2{x}_2^2}$
$=\frac{k_1}{k_2}\times {\left(\frac{k_2}{k_1}\right)}^2=\frac{k_2}{k_1}=\frac{3}{2}$
$\left[\because \frac{k_1}{k_2}=\frac{2}{3}\right]$