What will be the equivalent spring constant of the spring system shown in the figure ?

Options

A. `(1)/(2K_(1))+(K)/(K_(2))`
B. `(K_(1))/(2)+K_(2)`
C. `[(2)/(K_(1))+(1)/(K_(2))]^(-1)`
D. `[(1)/(2K_(1))+(1)/(K_(2))]^(-1)`

Answer

D

Explanation

Springs of springs constant `K_(1) and K_(1)` are joined in parallel.
`therefore` Their equivalent spring constant `=2K_(1)`
and `because ` springs of spring constant `2K_(1) and K_(2)` are joined in series, `(1)/(K_(s))=(1)/(2K_(1))+(1)/(K_(2))`
`therefore K_(s)=[(1)/(2K_(1))+(1)/(K_(2))]^(-1)`