Two springs have their force constant as k? and k? (k? k?). When they are stretched by the same force up to equilibrium:

Question

Two springs have their force constant as $k_{1}$ and $k_{2}$ $(k_{1} > k_{2})$ . When they are stretched by the same force up to equilibrium:

Smart Achievers · Accepted Answer

(3)

$F_{1} = F_{2}$

$∵$ $w_{1} = \frac{1}{2} k_{1} x_{1}^{2},$ $k_{1} x_{1} = k_{2} x_{2} = F$

$w_{1} = \frac{1}{2} k_{1} {[\frac{F}{k_{1}}]}^{2} = \frac{1}{2} \frac{F^{2}}{k_{1}}$

$∴$ $w_{2} = \frac{1}{2} \frac{F^{2}}{k_{2}}$

$∵$ $k_{1} > k_{2}$

$∴$ $w_{1} < w_{2}$

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