Question

Two elastic rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature is –

(a₁,a₂ = linear expansion coefficient, A₁, A₂ = Area of rods, Y₁,Y₂ = young modulus )

• A. $\frac{A_{1}}{A_{2}}$ = $\frac{\alpha_{1}Y_{1}}{\alpha_{2}Y_{2}}$
• B. $\frac{A_{1}}{A_{2}}$ = $\frac{L_{1}\alpha_{1}Y_{1}}{L_{2}\alpha_{2}Y_{2}}$
• C. $\frac{A_{1}}{A_{2}}$ = $\frac{L_{2}\alpha_{2}Y_{2}}{L_{1}\alpha_{1}Y_{1}}$
• D. $\frac{A_{1}}{A_{2}}$ = $\frac{\alpha_{2}Y_{2}}{\alpha_{1}Y_{1}}$

Answer 1

Answer: (D)

$\frac{A_{1}}{A_{2}}$ = $\frac{\alpha_{2}Y_{2}}{\alpha_{1}Y_{1}}$

Answer 2

Since tension in the two rods will be same, hence

A₁Y₁ a₁Dq = A₂Y₂a₂Dq

Ž A₁Y₁a₁ = A₂Y₂a₂