Question

Two springs of force constant 1000 N/m and 2000 N/m are streched 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

Answer: (A)

Forces are same $\therefore$ $\frac{k_1{x}_1}{k_2{x}_2}=1$ $\Rightarrow$ $\frac{k_1}{k_2}=\frac{x_2}{x_1}$ $\frac{x_2}{x_1}=\frac{1000}{2000}=\frac{1}{2}$ $\frac{U_1}{U_2}=\frac{\frac{1}{2}{k}_1{x}_1^2}{\frac{1}{2}{k}_2{x}_2^2}=\frac{k_1}{k_2}{\left[\frac{x_1}{x_2}\right]}^2$ $=\frac{1}{2}\times 4=\frac{2}{1}=2:1$