A planar frame is made of thin uniform rods. The length of section AB and EF is l 1 and its coefficient of linear expansion is α 1 . The length of section CD is l 2 and its coefficient of linear expansion is α 2 . CB and DE are of the same length having coefficient of linear expansion α 2 . Points A, B, E and F reside on same line, that is, sections AB and EF overlap. Then the ratio l 1 l 2 for which the distance between end A and end F remains the same at all temperatures is α 2 n α 1 then find the value of n .

Question

A planar frame is made of thin uniform rods. The length of section AB and EF is l 1 and its coefficient of linear expansion is α 1 . The length of section CD is l 2 and its coefficient of linear expansion is α 2 . CB and DE are of the same length having coefficient of linear expansion α 2 . Points A, B, E and F reside on same line, that is, sections AB and EF overlap. Then the ratio l 1 l 2 for which the distance between end A and end F remains the same at all temperatures is α 2 n α 1 then find the value of n .,

MARKS App · Accepted Answer

For distance between A and F to remain constant, extension in CD = extension in AB + extension in EF ∴ Δ l 2 = 2 Δ l 1 ⇒ l 2 α 2 Δ θ 2 = 2 l 1 α 1 Δ θ Or l 1 l 2 = α 2 2 α 1 n = 2

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