A 5.0cm diameter steel shaft has 0.10mm clearance all around its bushing at 20 degree Celsius.If the bushing temperature remains constant, at what...

The shaft will begin to bind when due to increasing temperature the diameter of shaft will increase to cover completely the clearance between the shaft and the bushing.

Given shaft diameter = D = 5 cm = 50 mm

Clearance between shaft and bushing = 0.1 mm all around

Initial temperature of shaft = t = 20 degree C

Linear coefficient of expansion = E = 11*18^-6 /degree C

As the clearance between shaft and bushing is all around, the increase in diameter of shaft (d) when the shaft just fill the clearance completely is twice the clearance. Thus:

d = 2*Clearance = 2*0.1 = 0.2 mm

The temperature rise (T) when the diameter D will expand by d is given by formula:

T = (d/D)/E = (0.2/50)/(11*10^-6) = 363.63 C

Temperature of shaft when it begins to bind is initial temperature (t) plus increase in temperature (T).

Therefore temperature of shaft = t +T = 20 + 363.63 = 383.63

= 383 C (rounding off to nearest unit number)

Answer:

The shaft will begin to bind when its temperature is 383 C.

None of the options given in the question corresponds to this.

Perhaps, by mistake, temperature given in option B) is given as 333 instead of 383.