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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

AI Generated Solution

To solve the problem, we need to determine the temperature to which the steel plate must be heated so that the diameter of the hole expands enough to accommodate a cylinder of diameter 1 cm. ### Step-by-Step Solution: 1. **Identify the Given Values:** - Diameter of the hole at 30°C, \( D_{hole} = 0.99970 \, \text{cm} \) - Diameter of the cylinder, \( D_{cylinder} = 1.00 \, \text{cm} \) - Coefficient of linear expansion for steel, \( \alpha = 1.1 \times 10^{-5} \, \text{°C}^{-1} \) ...
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