If `k_(s)` and `k_(p)` respectively are effective spring constant in series and parallel combination of springs as shown in figure, find `(k_(s))/(k_(p))`.

Options

A. `9/2`
B. `3/7`
C. `2/9`
D. `7/3`

Answer

C

Explanation

The effective spring constant `k_s` of this arrangement is
`1/(k_s) = 1/k + 1/(2k)`
`1/(k_s) = (2 + 1)/(2k) = 3/(2k)`
`k_s = (2k)/3`
The effective spring constant `k_p` of this arrangement is
`k_p = k_1 + k_2`
`= k = 2k = 3k `
`therefore (k_s)/(k_p) = (2k//3)/(3k) = 2/9`