To increase the length of a metal rod by 0.4 | vedclass

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Question

(C) The formula for linear expansion is given by $\Delta L = L \alpha \Delta T$, where $\Delta L$ is the change in length, $L$ is the original length,

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(C) The formula for linear expansion is given by $\Delta L = L \alpha \Delta T$, where $\Delta L$ is the change in length, $L$ is the original length, $\alpha$ is the coefficient of linear expansion, and $\Delta T$ is the change in temperature.Given that the length increases by $0.4 \%$, we have $\frac{\Delta L}{L} = 0.4 \% = \frac{0.4}{100} = 0.004$.The coefficient of linear expansion is $\alpha = 20 	imes 10^{-6} \ {}^{\circ}C^{-1}$.Substituting these values into the formula $\frac{\Delta L}{L} = \alpha \Delta T$:$0.004 = (20 	imes 10^{-6}) \Delta T$.Solving for $\Delta T$:$\Delta T = \frac{0.004}{20 	imes 10^{-6}} = \frac{4 	imes 10^{-3}}{20 	imes 10^{-6}} = \frac{1}{5} 	imes 10^3 = 0.2 	imes 1000 = 200 \ {}^{\circ}C$.Since the change in temperature in Celsius is equal to the change in temperature in Kelvin, $\Delta T = 200 \ K$.

To increase the length of a metal rod by $0.4 \%$, the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $= 20 \times 10^{-6} \ {}^{\circ}C^{-1}$) (in $K$)

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