$A$ 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 the 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
  $\frac{(Y_1 Y_2)^{1/2} A}{(L_1 + L_2)^{1/2}}$