Question

Two rods of length ₁ and₂ are made of materials whose coefficients of linear expansion are α₁ andα₂. If the difference between two lengths is independent of temperature then,

• A.
• B.
• C.
• D. $\frac { a _ { 1 } ^ { 2 } } { l _ { 1 } } = \frac { a _ { 2 } ^ { 2 } } { l _ { 2 } }$

Answer 1

Answer: (B)

Answer 2

L₁ = ₁ [1 + α₁ ∆T]

L₂ = ₂ [1 + α₂ ∆T]

L₁ – L₂ = (₁ - ₂) + (∆T) (₁ α₁ - ₂ α₂)

If L₁ – L₂ is to be independent of ∆T

Then ₁α₁ - ₂α₂ = 0 ⇒ $\frac { \ell _ { 1 } } { \ell _ { 2 } } = \frac { \alpha _ { 2 } } { \alpha _ { 1 } }$

Hence (2) is correct.