Q: Two rods of length L_{2} and coefficient of linear expansion α_{2} are connected freely to a third rod of length L_{1} of coefficient of linear expansion α_{1} to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of L_{1} which is horizontal. The apex of the isosceles triangle is to remain at a constant distance from the knife edge if

(a) $ \displaystyle \frac{L_1}{L_2} = \frac{\alpha_2}{\alpha_1} $

(b) $ \displaystyle \frac{L_1}{L_2} = \sqrt{\frac{\alpha_2}{\alpha_1}} $

(c) $ \displaystyle \frac{L_1}{L_2} = 2\frac{\alpha_2}{\alpha_1} $

(d) $ \displaystyle \frac{L_1}{L_2} = 2\sqrt{\frac{\alpha_2}{\alpha_1}} $

Ans: (d)