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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 0c-1]

Hermionie , 8 Years ago
Grade 11
anser 1 Answers
Rituraj Tiwari

Last Activity: 4 Years 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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