Question

Three rods of equal length are joined to form an equilateral triangle ABC and D is the midpoint of AB. The coefficient of linear expansion is α₁ for AB and α₂ for both AC and BC. If the distance DC remains constant for small changes in temperature, then what is the relation between

α₁ and α₂?

A. α₁ = α₂
B. α₁ = 2α₂
C. α₁ = 4α₂
D. α₁ = 1/2α₂

Answer 1

The relation between the coefficients of linear expansion, α₁ and α₂, is that they are equal.

The Correct Option is; A. α₁ = α₂.

Step-by-step explanation:

The relation between the coefficients of linear expansion, α₁ and α₂, can be determined using the fact that the distance DC remains constant for small temperature changes. Since D is the midpoint of AB in the equilateral triangle ABC, the expansion of AC and BC should be equal to maintain the equilateral shape. Therefore, we have:

AC = BC

Using the equation for linear thermal expansion, AL = αLAT, we can express AC and BC in terms of the changes in length and temperature:

AC = α₂L₂AT and BC = α₂L₂AT

Since AC = BC, we can equate the two expressions:

α₂L₂AT = α₂L₂AT

From this equation, we can conclude that α₁ = α₂.