A steel plug has a diameter of 5cm at 30°C. At what temperature will it fit exactly into a hole of constant diameter 4.997cm? 

Jamb 1978

A steel plug has a diameter of 5cm at 30°C. At what temperature will it fit exactly into a hole of constant diameter 4.997cm? 

(coefficient of linear expansion of steel is 11×10^-6 /°C)

A. 27.3°C

B. -27.3°C

C. -2.7°C

D. 7.32°C

E. 2.7°C

ANSWER: No Option is correct. The answer is -24.5°C

EXPLANATION: This is area expansion which requires a coefficient of area expansion. 

 The formula to use is 

B = ∆A/(A1×∆T)

Where; 

B —> coefficient of area expansion

∆A —> change in the area (A2-A1)

∆T —> change in temperature (T2-T1)

Note; Coefficient of area expansion is approximately two times the coefficient of linear expansion and the coefficient of volume expansion is approximately three times the coefficient of linear expansion.

So, you know what to do with the coefficient of linear expansion in the question, and also note that the question says diameter, you have to find the area using the diameter given.

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