At 30^∘ C, the hole in a steel plate has diameter of 0.99970 cm. A cylinder of diameter exactly

step 1 Hello students in this question we have given the temperature t1 equals to 30 degree centigrade

At 30^∘ C, the hole in a steel plate has diameter of 0.99970...

At $30^{\circ} \mathrm{C}$, the hole in a steel plate has diameter of $0.99970$ $\mathrm{cm}$. A cylinder of diameter exactly $1 \mathrm{~cm}$ at $30^{\circ} \mathrm{C}$ is to be slide into the hole. To what temperature the plate must be heated ? (Given : $\alpha_{\text {steel }}=1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ ) (a) $58^{\circ} \mathrm{C}$ (b) $55^{\circ} \mathrm{C}$ (c) $57.3^{\circ} \mathrm{C}$ (d) $60^{\circ} \mathrm{C}$

At $30^{\circ} \mathrm{C}$, the hole in a steel plate has diameter of $0.99970$ $\mathrm{cm}$. A cylinder of diameter exactly $1 \mathrm{~cm}$ at $30^{\circ} \mathrm{C}$ is to be slide into the hole. To what temperature the plate must be heated ? (Given : $\alpha_{\text {steel }}=1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ )
(a) $58^{\circ} \mathrm{C}$
(b) $55^{\circ} \mathrm{C}$
(c) $57.3^{\circ} \mathrm{C}$
(d) $60^{\circ} \mathrm{C}$

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Key Concepts

Linear Thermal Expansion

This concept refers to the phenomenon where materials change their dimensions (length, area, or volume) as a function of temperature. When a material is heated, its dimensions typically increase, and this change is proportional to the original dimension, the temperature change, and the material's coefficient of thermal expansion.

Coefficient of Thermal Expansion

This is a material-specific constant that quantifies the rate at which a material’s dimensions expand or contract with temperature changes. It is used to calculate the new dimensions of an object when it undergoes a temperature change by multiplying it with the original dimension and the temperature difference.

Thermal Fit and Tolerance Adjustments

This concept involves applying the principles of thermal expansion to ensure parts will properly fit together under varying temperature conditions. It requires adjusting the dimensions of one or both components through temperature changes so that the engineered tolerances are met, ensuring functional assembly.

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