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At 30^(@)C, the hole in a steel plate ha...

At `30^(@)`C, the hole in a steel plate has diameter of 0.99970 cm. A cylinder of diameter exactly 1 cm at `30^(@)`C is to be slide into the hole. To what temperature the plate must be heated?
(Given `alpha_(Steel)=1.1xx10^(-5^(@))C^(-1)`

A

`58^(@)C`

B

`55^(@)C`

C

`57.3^(@)C`

D

`60^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
C
As, `Delta l= 1- 0.99970= 0.00030cm`
Also, `Delta l= alpha//Delta t`
`rArr Delta t= (Delta l)/(alpha l)= (0.0003)/(1.1 xx 10^(-5) xx 0.9997)= 27.3^(@)C`
So, plate temperature must be ralsed to
`30^(@)C + 27.3^(@)C= 57.3^(@)C`
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