A metal wire of length \[{{L}_{1}}\]and area of cross-section A is attached to a rigid support. Another metal wire of length \[{{L}_{2}}\] and of the same cross-sectional area is attached to the free end of the first wire. A body of mass M is then suspended from the free end of the second wire. If \[{{Y}_{1}}\]and \[{{Y}_{2}}\] are the young's moduli of the wires respectively, the effective force constant of the system of two wires is

• A. \[\frac{({{Y}_{1}}{{Y}_{2}})A}{2({{Y}_{1}}{{L}_{2}}+{{Y}_{2}}{{L}_{1}})}\]
• B. \[\frac{({{Y}_{1}}{{Y}_{2}})A}{{{({{L}_{1}}{{L}_{2}})}^{1/2}}}\]
• C. \[\frac{({{Y}_{1}}{{Y}_{2}})A}{{{Y}_{1}}{{L}_{2}}+{{Y}_{2}}{{L}_{1}}}\]
• D. \[\frac{{{({{Y}_{1}}{{Y}_{2}})}^{1/2}}A}{{{({{L}_{2}}{{L}_{1}})}^{1/2}}}\]