A planar lamina is made of thin uniform rods. The length of section AB and EF is L₁ and its coefficient is α₁. The length of CD is L₂ and its coefficient is α₂. CB and DE are of same length having coefficient $\frac{α_{1}}{α_{2}} = 3.5$ Points A, B, E and F reside on the same line that is sections AB and EF overlap. Then find the ratio of $\frac{l_{2}}{l_{1}}$ for which the distance between end A and end F remain same at all temperatures

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answer is C.

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Detailed Solution

Since AF is constant, $2{L_1}{\alpha _1} = {L_2}{\alpha _2}$

where L₁ = EB and L₂ = CD

$\frac{{{\alpha _1}}}{{{\alpha _2}}} = \frac{7}{2}\therefore \frac{{{L_2}}}{{{L_1}}} = 2\left( {\frac{{{\alpha _1}}}{{{\alpha _2}}}} \right) = 7$

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