Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are $Y_1$ and $Y_2$. The combination behaves as a single wire then its Young's modulus is:

• A

  $Y=\frac{2Y_1{Y}_2}{3\left(Y_1+Y_2\right)}$
• Correct answer
  B

  $Y=\frac{2Y_1{Y}_2}{Y_1+Y_2}$
• C

  $Y=\frac{Y_1{Y}_2}{2\left(Y_1+Y_2\right)}$
• D

  $Y=\frac{Y_1{Y}_2}{Y_1+Y_2}$

Hence, the correct answer is option: 'B'.