If two springs A and B with spring constants 2k and k, are stretched separately by same suspended weight, then the ratio between the work done in stretching A and B is

If two springs A and B with spring constants 2k and k, are stretched s

1.	If two springs A and B with spring constants 2k and k, are stretched separately by same suspended weight, then the ratio between the work done in stretching A and B is
Answer» `1:2` `1:4` `4:1` ` 2:1` SOLUTION :For SPRING `A , mg = k_A x_A` For spring `B, mg = k_B x_B` SINCE both the springs A and B are suspended by same weight, therefore, `k_Ax_A = k_Bx_B " or " (k_A)/(k_B) = (x_B)/(x_A) ""…(i)` `:.` Ratio of work done in stretching A and B is `(W_A)/(W_B) = (1/2k_A x_A^2)/(1/2 k_B x_B^2) = (k_A)/(k_B) ((x_A)/(x_B))^(2) = (k_A)/(k_B) ((k_B)/(k_A))^(2) ""` (USING (i)) `= (k_B)/(k_A) = (k)/(2k) = 1/2` .