Question

Two identical rods of identical dimensions and Young’s moduli Y₁ and Y₂ are joined end to end. The equivalent young’s modulus for the composite rod is

• A. $\frac{Y_{1} + Y_{2}}{2}$
• B. $\frac{2Y_{1}Y_{2}}{Y_{1} + Y_{2}}$
• C. Y₁ + Y₂
• D. $\frac{Y_{1}Y_{2}}{Y_{1} + Y_{2}}$

Answer 1

Answer: (B)

$\frac{2Y_{1}Y_{2}}{Y_{1} + Y_{2}}$

Answer 2

∆l₁ + ∆l₂ = ∆l or $\frac{Fl}{Y_{1}A} + \frac{Fl}{Y_{2}A} = \frac{F2l}{YA}$

or Y = $\frac{2Y_{1}Y_{2}}{Y_{1} + Y_{2}}$