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A copper collar is to fit tightly about ...

A copper collar is to fit tightly about a steel shaft that has a diameter of 6 cm at `20^@C`. The inside diameter of the copper collar at the temperature is `5.98cm`
If the breaking stress of copper is `230 N//m^2`, at what temperature will the copper collar break as it cools?

A

`20^@C`

B

`47^@C`

C

`94^@C`

D

`217^@C`

Text Solution

Verified by Experts

The correct Answer is:
C
`alphaLDeltaT+L((F)/(A))/(alphaY)=0`
`DeltaT=((F)/(A))/(alphaY)=(230xx10^6(N)/(m^2))/((17xx10^-6K^-1)(110xx10^9(N)/(m^2))`
`=-123K=-123^@C`
Final temperature at which the copper collar breaks
`T_f=T_i+DeltaT=217^@C-123^@C=94^@C`
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