The difference in length between two rods A a | vedclass

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(B) Given: The difference in length $\Delta l = l_{A} - l_{B} = 60 	ext{ cm}$ is constant at all temperatures.This implies that the change in length

Vedclass · Accepted Answer

$l_{A} = 180 	ext{ cm}, l_{B} = 120 	ext{ cm}$

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(B) Given: The difference in length $\Delta l = l_{A} - l_{B} = 60 	ext{ cm}$ is constant at all temperatures.This implies that the change in length for both rods must be equal for any temperature change $\Delta T$.$\Delta l_{A} = \Delta l_{B}$$l_{A} \alpha_{A} \Delta T = l_{B} \alpha_{B} \Delta T$$l_{A} \alpha_{A} = l_{B} \alpha_{B}$Substituting the given values:$l_{A} (18 	imes 10^{-6}) = l_{B} (27 	imes 10^{-6})$$l_{A} (18) = l_{B} (27)$$l_{A} = \frac{27}{18} l_{B} = 1.5 l_{B}$We know $l_{A} - l_{B} = 60 	ext{ cm}$.Substituting $l_{A} = 1.5 l_{B}$:$1.5 l_{B} - l_{B} = 60 	ext{ cm}$$0.5 l_{B} = 60 	ext{ cm}$$l_{B} = 120 	ext{ cm}$Then,$l_{A} = 1.5 	imes 120 = 180 	ext{ cm}$.

The difference in length between two rods $A$ and $B$ is $60 \text{ cm}$ at all temperatures. If $\alpha_{A} = 18 \times 10^{-6} /^{\circ}\text{C}$ and $\alpha_{B} = 27 \times 10^{-6} /^{\circ}\text{C}$,the lengths of the two rods are:

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