An isosceles triangle is formed with a thin rod of length l1 and coefficient of linear expansion α1, as the base and two thin rods each of lenglh /, and coefficient of linear expansion α2, as the two sides. The distance between the apex and the midpoint of the base remain unchanged as the temperature is varied. The ratio of lengths l1l2 is
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a
2α1α2
b
α2α1
c
2α2α1
d
12α2α1
answer is C.
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Detailed Solution
The distance between the apex and the midpoint of the base, using Pythagoras theorem l = (l2)2-(l12)2or l2 = (l2)2-(l12)2------------(i)Differentiating (i) w.r.t. temperature 0 = 2l2×dl2dT-2(l12).12×dl1dTl12×l1α1 =2l2×l2α2(l1l2)2 = 4α2α1 ⇒ l1l2 = 2α2α1