Two rods of lengths l1 and l2 are made of materials whose coeffic

Question

Two rods of lengths

l_{1}

and

l_{2}

are made of materials whose coefficients of linear expansion are

α_{1}

and

α_{2}

. If the difference between the two lengths is independent of temperature, then

Options:

A . l1l2=α1α2

B . l1l2=α2α1

C . l22α1=l21α2

D . α21l1=α22l2

Answer: Option B
:
B

L_{1} = l 1 [1 + α_{1} Δ T] L_{2} = l 2 [1 + α_{2} Δ T] L_{1} + L_{2} = (l_{1} + l 2) + (Δ T) (l_{1} α_{1} - l_{2} α_{2}) I f L_{1} - L_{2} i s t o b e i n d e p e n d e n t o f Δ T, t h e n l_{1} α_{1} - l_{2} α_{2} = 0 \Rightarrow \frac{l_{1}}{l 2} = \frac{α_{1}}{α_{2}} \frac{l_{1}}{l 2} = \frac{α_{2}}{α_{1}}

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