Two springs A and B are identical but A is harder than B(kA kB). Let WA and WB represent the work done when the springs are stretched through the same distance and WA' and WB' are the work done when these are stretched by equal forces, then which of the following is true?

Question

Two springs A and B are identical but A is harder than B(kA >kB). Let WA and WB represent the work done when the springs are stretched through the same distance and WA' and WB' are the work done when these are stretched by equal forces, then which of the following is true? (A) WA>WB and WA'=WB' (B) WA >WB and WA'< WB' (C) WA > WB and WA' > WB' (D) WA< WB and WA'< WB'

Tardigrade Admin · Accepted Answer

Work done in stretching a spring W=(1/2) k x2 Here, WA=(1/2) kA xA2 and WB=(1/2) kB xB2 As xA=xB and kA>kB ∴ WA>WB Similarly, when forces are equal FA=FB kA xA=kB xB ... (i) As kA>kB ∴ xA< xB ldots (ii) Now, W'A=(1/2)(kA xA) xA and W'B=(1/2)(kB xB) xB From Eqs. (i) and (ii), we conclude that W'A< W'B

$W_{A} > W_{B}$ and $W_{A}^{'} = W_{B}^{'}$

$W_{A} > W_{B}$ and $W_{A}^{'} < W_{B}^{'}$

$W_{A} > W_{B}$ and $W_{A}^{'} > W_{B}^{'}$

$W_{A} < W_{B}$ and $W_{A}^{'} < W_{B}^{'}$

Q. Two springs A and B are identical but A is harder than B(kA​>kB​). Let WA​ and WB​ represent the work done when the springs are stretched through the same distance and WA′​ and WB′​ are the work done when these are stretched by equal forces, then which of the following is true?

WA​>WB​ and WA′​=WB′​

WA​>WB​ and WA′​<WB′​

WA​>WB​ and WA′​>WB′​

WA​<WB​ and WA′​<WB′​

$W_{A} > W_{B}$ and $W_{A}^{'} = W_{B}^{'}$

$W_{A} > W_{B}$ and $W_{A}^{'} < W_{B}^{'}$

$W_{A} > W_{B}$ and $W_{A}^{'} > W_{B}^{'}$

$W_{A} < W_{B}$ and $W_{A}^{'} < W_{B}^{'}$