Question

Two rods with identical dimension but different Young’s modulus of 4 x 10¹¹ Nm^-2 and 6 x 10¹¹Nm^-2 are joined end to end. An equivalent rod of identical dimensions is to be constructed. The Young’s modulus of the equivalent rod will be

(1) 5 x 10¹¹ Nm^-2 

(2) 2.4 x 10¹¹ Nm^-2

(3) 10 x 10¹¹ Nm^-2 

(4) 12 x 10¹¹ Nm^-2

Answer 1

(2) 2.4 x 10¹¹ Nm^-2

Let L and A be the length and area of cross-section of each rod. Then

Extension in the equivalent rod is also (Δl)₁ + (Δl)₂ . Let Y be Young’s modulus of the equivalent rod. Then

From Eqns (1), (2) and (3) we have

Substituting give values of Y₁ and Y₂ we have