Two springs A and B are identical but A is harder than B `(k_A > k_B)`. Let Wand Wg represent the work done when the springs are stretched through the same distance and `W_A^. and W_B^.` are the work done when these are stretched by equal forces, then which of the following is true? 

Options

A. `W_A gt W_B and W_A^. = W_B^.`
B. `W_Agt W_B and W_A^. lt W_B^.`
C. `W_A gt W_B and W_A^. gt W_B^.`
D. `W_A lt W_B and W_A^. lt W_B^.`

Answer

B

Explanation

`k_A > k_B`, x is the same
`:. 1/2 k_A x^2 > 1/2 k_B x^2 " or " W_A > W_B`
Process are the same,
`:. k_A x_A = k_B x_B . Ask_A > k_B, so x_A < x_B`
`W_A^.= 1/2 (k_A x_A) x_A and W_B^. = 1/2 (k_B x_B) x_B , :. W_A^. < W_B^.`.