Question

Two springs $A$ and $B$ are identical but $A$ is harder than $B(k_A>k_B)$. Let $W_A$ and $W_B$ represent the work done when the springs are stretched through the same of the distance and $W_A^{\prime }$ and $W_B^{\prime }$ are the work done when these are stretched by equal forces then which of the following is true:

Answer 1

$k_A>k_B$

When stretched by same distance-

$U=\frac{1}{2}k{x}^2=W$

$⟹W_A>W_B$ since $k_A>k_B$

When stretched by same force-

$F=kx⟹x=\frac{F}{k}$

$W=\frac{1}{2}k{x}^2=\frac{F^2}{2k}$

$⟹W\propto \frac{1}{k}$

$⟹W_A^{\prime }<W_B^{\prime }$ since $k_A>k_B$