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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 that temperature is 5.98 cm.
To what temperature must the copper collar be raised so that it will just slip on the steel shaft, assuming the steel shaft remains at `20^(@)C`? `(alpha_("cooper")=17 times 10^(-6)K^(-1))`

A

`324^(@)C`

B

`21.7^(@)C`

C

`217^(@)C`

D

`32.4^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
C
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Diameter of a brass disc at 30^(@)C is 10 cm. What will be the increase in area of the disc at 70^(@)C ? alpha for brass =18 times 10^(-6@)C^(-1) .

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Knowledge Check

  • 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 that temperature is 5.98 cm. The tensile stress in the copper collar when its temperature returns to 20^(@)C is (Y=11 times 10^(10)N*m^(-2))

    A
    `1.34 times 10^(5)N*m^(-2)`
    B
    `3.68 times 10^(-12)N*m^(-2)`
    C
    `3.68 times 10^(8)N*m^(-2)`
    D
    `1.24 times 10^(-12)N*m^(-2)`

  • 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 that temperature is 5.98 cm. 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`

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