The length of a metal rod at 30^{circ} C is 3 | vedclass

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(C) The formula for the coefficient of linear expansion $\alpha$ is given by: $\alpha = \frac{\Delta L}{L \Delta T}$ Given: Initial length $L = 30 \ c

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$12 	imes 10^{-6} /{ }^{\circ} C$

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(C) The formula for the coefficient of linear expansion $\alpha$ is given by: $\alpha = \frac{\Delta L}{L \Delta T}$ Given: Initial length $L = 30 \ cm$ Change in length $\Delta L = 0.027 \ cm$ Initial temperature $T_1 = 30^{\circ} C$ Final temperature $T_2 = 105^{\circ} C$ Change in temperature $\Delta T = T_2 - T_1 = 105^{\circ} C - 30^{\circ} C = 75^{\circ} C$ Substituting the values into the formula: $\alpha = \frac{0.027}{30 	imes 75}$ $\alpha = \frac{0.027}{2250}$ $\alpha = 0.000012 /{ }^{\circ} C$ $\alpha = 12 	imes 10^{-6} /{ }^{\circ} C$

The length of a metal rod at $30^{\circ} C$ is $30 \ cm$. If its temperature is raised to $105^{\circ} C$, its length is increased by $0.027 \ cm$. Then the coefficient of linear expansion of the metal is

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