Two springs A and B are identical except that A is stiffer than B i.e., `k_A > k_B`. If the two springs are stretched by the same force, then 

Options

A. more work is done on B i.e.,`W_B gt W_A`
B. more work is done on A i.e., `W_A gt W_B`
C. work done on A and B are equal
D. work done depends upon the way in which they are stretched

Answer

A

Explanation

`F = k_Ax_A = k_Bx_B " or " (x_A)/(x_B) = (k_B)/(k_A) " " ….(i)`
As `W_A = 1/2 k_A x_A^2 and W_B = 1/2 k_B x_B^2`
`:. (W_A)/(W_B) = (k_A)/(k_B) (x_A^2)/(x_B^2) = (k_A)/(k_B) (k_B^2)/(k_A^2) = (k_B)/(k_A) " (Using (i))"`
Hence, `W_B > W_A`. So more work is done on B.