Question

two springs of spring constant 1500N/m and 3000N/m respectively are stretched with same force. they will have potential energies in the ratio

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{U}=\frac{1}{2}{\mathrm{kx}}^2 \\ \mathrm{but},\mathrm{x}=\frac{\mathrm{F}}{\mathrm{k}} \\ \Rightarrow \mathrm{U}=\frac{1}{2}\mathrm{k}{\left(\frac{\mathrm{F}}{\mathrm{k}}\right)}^2 \\ \Rightarrow \mathrm{U}=\frac{{\mathrm{F}}^2}{2\mathrm{k}} \\ \Rightarrow \frac{{\mathrm{U}}_1}{{\mathrm{U}}_2}=\frac{{\mathrm{k}}_2}{{\mathrm{k}}_1} \\ \Rightarrow \frac{{\mathrm{U}}_1}{{\mathrm{U}}_2}=\frac{3000}{1500} \\ \Rightarrow \frac{{\mathrm{U}}_1}{{\mathrm{U}}_2}=\frac{2}{1} \end{gathered}$$