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

Options

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

Answer

C

Explanation

In the arrangement shown in Fig (i) the two springs are in series. The effective spring constant `k_(s)` of this
`(1)/(k_(s))=(1)/(k)+(1)/(2k)=(2+1)/(2k)=(3)/(2k)" "[because k_(s) = (2k)/(3)]`
In the arrangement shown in Fig. (ii) the two springs are in parallel. The effective spring constant `k_(p)` of this arrangement is
`k_(p) = k_(1) + k_(2) = k + 2k = 3k`
Thus, `(k_(s))/(k_(p))=(2k//3)/(3k)=(2)/(9)`