A metal cylinder of radius R is placed on a wooden plank BD. The plank is kept horizontal suspended with the help of two identical string AB and CD each of length L. The temperature coefficient of linear expansion of the cylinder and the strings are α1 and α2 respectively. Angle θ shown in the figure is 300 . It was found that with change in temperature the center of the cylinder did not move. Then the ratio α1α2 is ? If it is know that L = 4R. Assume that change in value of θ is negligible for small temperature changes.

Question

A metal cylinder of radius R is placed on a wooden plank BD. The plank is kept horizontal suspended with the help of two identical string AB and CD each of length L. The temperature coefficient of linear expansion of the cylinder and the strings are α1  and α2  respectively. Angle θ  shown in the figure is 300 . It was found that with change in temperature the center of the cylinder did not move. Then the ratio α1α2 is ? If it is know that L = 4R. Assume that change in value of θ  is negligible for small temperature changes.

Infinity Learn · Accepted Answer

Let change in temperature be ΔTLength of a string changes by ΔL=Lα2ΔT The wooden plank descends by Δy=ΔLsinθΔy=2ΔL[∵sinθ=12] Change in radius of the ball: ΔR=Rα1ΔTThe center of the ball will not move if Δy=ΔR⇒2Lα2ΔT=Rα1ΔT⇒8Rα2=Rα1⇒α1α2=81

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