A rod of length 20 , cm is made of metal A. I | vedclass

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(B) The formula for linear expansion is $\Delta L = L_0 \alpha \Delta 	heta$.For rod $A$: $0.075 = 20 	imes \alpha_A 	imes (100 - 0) \implies \alph

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(B) The formula for linear expansion is $\Delta L = L_0 \alpha \Delta 	heta$.For rod $A$: $0.075 = 20 	imes \alpha_A 	imes (100 - 0) \implies \alpha_A = \frac{0.075}{2000} = 3.75 	imes 10^{-5} /^{\circ}C$.For rod $B$: $0.045 = 20 	imes \alpha_B 	imes (100 - 0) \implies \alpha_B = \frac{0.045}{2000} = 2.25 	imes 10^{-5} /^{\circ}C$.For the composite rod,let the length of metal $A$ be $x$ and the length of metal $B$ be $(20 - x)$.The total expansion is the sum of expansions of the two parts:$\Delta L_{total} = (x \alpha_A \Delta 	heta) + ((20 - x) \alpha_B \Delta 	heta)$$0.060 = [x(3.75 	imes 10^{-5}) + (20 - x)(2.25 	imes 10^{-5})] 	imes 100$$0.060 = 0.00375x + 0.045 - 0.00225x$$0.015 = 0.0015x$$x = \frac{0.015}{0.0015} = 10 \, cm$.

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