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Q.

In the shown planar frame made of thin uniform rods, the' length of section AB and EF is l1 and its thermal linear coefficient of expansion is α1. The length of section CD is l2 and its thermal linear coefficient of expansion is α2. CB and DE are of same length having thermal linear coefficient of expansion α2. Points A, B, E and F reside on same line, that is, sections AB and EF overlap. Then the ratio l1l2 for which the distance between end A and end F remains the same at all temperatures, is:

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a

α22α1

b

2α2α1

c

2α1α2

d

α12α2

answer is A.

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Detailed Solution

For distance between A and F to remain constant, extension in CD = extension in AB + extension in EF∴ ∆l2 = 2∆l1 ⇒ l2α2∆θ2 = 2l1α1∆θor l1l2 = α22α1

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In the shown planar frame made of thin uniform rods, the' length of section AB and EF is l1 and its thermal linear coefficient of expansion is α1. The length of section CD is l2 and its thermal linear coefficient of expansion is α2. CB and DE are of same length having thermal linear coefficient of expansion α2. Points A, B, E and F reside on same line, that is, sections AB and EF overlap. Then the ratio l1l2 for which the distance between end A and end F remains the same at all temperatures, is: