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)

Energy of spring $U=\frac{1}{2}k{x}^2$
and force $f=kx$
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 $\frac{f_1^2}{k_1}=\frac{f_2^2}{k_2}$
$\Rightarrow \frac{f_1}{f_2}=\frac{\sqrt{k_1}}{\sqrt{k_2}}$