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 $$30^{\circ}C$$. At what temperature, the same for ball and plate, will the ball just pass through the hole ?

Solution

## Since the linear expansion is given by the expression $$\Delta l=l\alpha \Delta T$$Hence, in the given situation, since both iron ball and brass plate will expand. Hence,$$d({ \alpha }_{ Brass }-{ \alpha }_{ Iron })\Delta T=0.01mm$$$$60({ \alpha }_{ Brass }-{ \alpha }_{ Iron })\Delta T=0.01$$$$60(19-12) { 10 }^{ -6 }(T-30)=0.01$$$$T={ 50.8 }^{ 0 }C$$Answer is $${ 50.8 }^{ 0 }C$$Physics

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