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 

Options

A. `1:2`
B. `1:4`
C. `4:1`
D. ` 2:1`

Answer

A

Explanation

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` .