Question

Two springs have their force constants $K_1$ and $K_2$. Both are stretched till their elastic energies are equal. Then, ratio of stretching forces $F_1/F_2$ is equal to :

• A. $K_1/K_2$
• B. $K_1:K_2$
• C. $\sqrt{K_1}:\sqrt{K_2}$
• D. ${K_1}^2:{K_2}^2$

Answer 1

The correct option is C $\sqrt{K_1}:\sqrt{K_2}$

Potential energy,

$U=\frac{1}{2}K{X}^2$. . . . . .(1)

Ratio $\frac{U_1}{U_1}=\frac{U}{U}=\frac{K_1{X}_1^2/2}{K_2{X}_2^2/2}$

$\frac{X_1}{X_2}=\sqrt{\frac{K_2}{K_1}}$. . . . . . .(2)

Force ratio, $\frac{F_1}{F_2}=\frac{K_1{X}_1}{K_2{X}_2}$

$\frac{F_1}{F_2}=\frac{K_1}{K_2}\sqrt{\frac{K_2}{K_1}}=\sqrt{\frac{K_1}{K_2}}$

$F_1:F_2=\sqrt{K_1}:\sqrt{K_2}$

The correct option is C.