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A large steel wheel is to be fitted on to a shaft of the same material. At 27c the outer diameter of the shaft is 8.70cm and the diameter of the central hole in the wheel is 8.69cm. The shaft is cooled using dry ice. At what temp. of the shaft does the wheel slip on the shaft? [coeff of linear expansion of steel is 1.20x10 -5 0 c -1 ]

A large steel wheel is to be fitted on to a shaft of the same material. At 27c the outer diameter of the shaft is 8.70cm and the diameter of the central hole in the wheel is 8.69cm. The shaft is cooled using dry ice. At what temp. of the shaft does the wheel slip on the shaft?
[coeff of linear expansion of steel is 1.20x10-5 0c-1]

Grade:11

1 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
one year ago
Coefficient of linear expansion of steel (a) = 1.2 × 10^-5 /K
outer diameter ( D1) = 8.70 cm
Inner diameter ( D2) = 8.69 cm
T1 = 27 + 273 = 300 K
T2 = ?
Change in due to cooling ,
D2 = D1 ( 1 + a ∆T )
8.69 = 8.70 [ 1 + 1.2 × 10^-5 × ( T2 - 300)]
(8.69 - 8.70) = 8.7 × 1.2 × 10^-5 × (T2 - 300)
T2 - 300 = -0.01/8.7 × 1.2 × 10^-5
T2 = 300 - 95.78
= 204.22 K
in clecius ,
C = 273 - 204.22 = 68.78°C ≈ 60°C

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