An iron ball has a diameter of 6 cm and is 0.010 mm too large to pass through a hole in a brass plate when the ball and plate are at a temperature of 
. At what temperature, the same for ball and plate, will the ball just pass through the hole? ( 
and 
)
Text Solution
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Let 
stand for the iron ball and 
stand for the brass plate. 
and 
at 
. Since the brass plate expands uniformly, the hole must expand in the same proportion. Then heating both the ball and the plate leads to increases in the diameters of the ball and the hole, with the hole increasing more, since 
. We require 
; 
. We can approximate 
in this formula by 6 cm 
. Then
On solving, 
, and finally 
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