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Three metal rods of the same length and area of cross section form an equilateral triangle as shown in Fig. D is the mid-point of side BC. If AD is independent for small change in temperature, then ( $α_{1}$ is the coefficient of linear expansion for rod BC and $α_{2}$ for rods AB and AC).

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α1=2α2

α1=α22

α2=α1

α1=4α2

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detailed solution

Correct option is D

AD2=l2-l24=l(1+α2t)2-l2(1+α1t)2,expanding binomially and neglecting α2 and higher order terms, keeping AD2 independent of t.We get α1=4α2

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Three metal rods of the same length and area of cross section form an equilateral triangle as shown in Fig. D is the mid-point of side BC. If AD is independent for small change in temperature, then (α1 is the coefficient of linear expansion for rod BC and α2 for rods AB and AC).

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Three metal rods of the same length and area of cross section form an equilateral triangle as shown in Fig. D is the mid-point of side BC. If AD is independent for small change in temperature, then ( $α_{1}$ is the coefficient of linear expansion for rod BC and $α_{2}$ for rods AB and AC).