If a cylinder of diameter 10 cm at 30c is to be solid into a...

If a cylinder of diameter 1.0 cm at 30°C is to be solid into a hole of diameter 0.9997 cm in a steel plate at the same temperature, then minimum required rise in the temperature of the plate is : (Coefficient of linear expansion of steel 12*10^-6 (a) 25°C (b) 35°C (c) 45°C (d) 55°C

A cylinder of diameter $1.00000 \mathrm{~cm}$ at $30^{\circ} \mathrm{C}$ is to be slid into a hole in a steel plate. The hole has a diameter of $0.99970 \mathrm{~cm}$ at 30 ${ }^{\circ} \mathrm{C}$. To what temperature must the plate be heated? For steel, $\alpha=$ $1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ The plate will expand in the same way whether or not there is a hole in it. Hence, the hole expands in the same way a circle of steel filling it would expand. We want the diameter of the hole to change by $$ \Delta L=(1.00000-0.99970) \mathrm{cm}=0.00030 \mathrm{~cm} $$ Using $\Delta L=\alpha L \Delta T$, $$ \Delta T=\frac{\Delta L}{\alpha L_{0}}=\frac{0.00030 \mathrm{~cm}}{\left(1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\right)(0.99970 \mathrm{~cm})}=27^{\circ} \mathrm{C} $$ The temperature of the plate must be $30+27=57^{\circ} \mathrm{C}$.

Question

If a cylinder of diameter 1.0 cm at 30°C is to be solid into a hole of diameter 0.9997 cm in a steel plate at the same temperature, then minimum required rise in the temperature of the plate is : (Coefficient of linear expansion of steel 12*10^-6 (a) 25°C (b) 35°C (c) 45°C (d) 55°C

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