Question

There are two rods of length a1 and a2 and the coefficient of linear expansions are «1 and «w: respectively. Find the equivalent coefficient of thermal expansion for their combination in senes.

Answer 1

Answer:

option d................

Answer 2

There are two rods of length l₁ and l₂ and coefficient of linear expansions are α₁ and α₂ respectively.

To find : The equivalent coefficient of thermal expansion for their combination in series.

solution : here, equivalent length at 0° C , l₀ = l₁ + l₂

equivalent length at t°C, l = l₀(1 + α∆T)

here, l = l₁' + l₂'

= l₁(1 + α₁∆T) + l₂(1 + α₂∆T)

= (l₁ + l₂) + (l₁α₁ + l₂α₂)∆T

now, (l₁ + l₂) + (l₁α₁ + l₂α₂)∆T = (l₁ + l₂)(1 + α∆T)

⇒1 + [(l₁α₁ + l₂α₂)/(l₁ + l₂)]∆T = 1 + α∆T

⇒α = (l₁α₁ + l₂α₂)/(l₁ + l₂)

Therefore equivalent coefficient of expansion for the their combination is (l₁α₁ + l₂α₂)/(l₁ + l₂)