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 α$$1$$. The length of section CD is $$l2$$ and its thermal linear coefficient of expansion is α$$2$$. CB and DE are of same length having thermal linear coefficient of expansion α$$2$$. 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:

Question

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 α$$1$$. The length of section CD is $$l2$$ and its thermal linear coefficient of expansion is α$$2$$. CB and DE are of same length having thermal linear coefficient of expansion α$$2$$. 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:

Infinity Learn · Accepted Answer

For distance between A and F to remain constant, extension in CD $$=$$ extension in AB $$+$$ extension in EF∴ ∆$$l2$$ $$=$$ $$2$$∆$$l1$$    ⇒ $$l2$$α$$2$$∆θ$$2$$ $$=$$ $$2l1$$α$$1$$∆θor $$l1l2$$  $$=$$ α$$22$$α$$1$$

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