Question

The force constants of two springs are $k_{1}$ and $k_{2}$ respectively. Both are stretched till their potential energies are equal. The forces $f_{1}$ and $f_{2}$ applied on them are in the ratio

• A. $k_{1} : k_{2}$
• B. $k_{2} : k_{1}$
• C. $\sqrt{k_{1}} : \sqrt{k_{2}}$
• D. $\sqrt{k_{2}} : \sqrt{k_{1}}$

Answer 1

Answer: (C)

$\sqrt{k_{1}} : \sqrt{k_{2}}$

Answer 2

Energy of spring $U=\frac{1}{2} k x^{2}$ and force $f=k x$ From these two, we get $U=\frac{1}{2} k \frac{f^{2}}{k^{2}}=\frac{1}{2} \frac{f^{2}}{k}$ $\because$ Energies are equal, therefore $\frac{f_{1}^{2}}{k_{1}}=\frac{f_{2}^{2}}{k_{2}}$ $\Rightarrow \frac{f_{1}}{f_{2}}=\frac{\sqrt{k_{1}}}{\sqrt{k_{2}}}$