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Question

An iron ball has a diameter of 6 cm and is 0.010 mm too large to pass through a hole in a brass when the ball and plate are at a temperature of 30C. At what temperature, the same for ball and plate, will the ball just pass through the hole ?

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Solution

Since the linear expansion is given by the expression Δl=lαΔT

Hence, in the given situation, since both iron ball and brass plate will expand. Hence,

d(αBrassαIron)ΔT=0.01mm

60(αBrassαIron)ΔT=0.01

60(1912)106(T30)=0.01

T=50.80C

Answer is 50.80C

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