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A steel ring is heated up to 95^(@)C to ...

A steel ring is heated up to `95^(@)C` to fit exacty on the outer surface of an iron cylinder of diameter 10 cm at `20^(@)C.` After fitting, the ring is cooled so that the system attains a temperature `20^(@)C.` What is the thermal stress of the ring? [Young's modulus of steel =`21 times 10^(5)kg*cm^(-2) " and " alpha` for steel `=12 times 10^(-6@)C^(-1).]`

Text Solution

Verified by Experts

Thermal stress `=Yat=21 times 10^(5) times 12 times 10^(-6) times 75`
`" "=1890 kg*cm^(-2)`
`" "=1890 times 1000 times 980 dyn*cm^(-2)`
`" "=1.8522 times 10^(9) dyn*cm^(-2).`
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