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# Two iron rods have their lengths in the ratio 5:3 and diameters in the ratio 2:1. When the rods are heated from  ${30}^{0}C$ to ${100}^{0}C$  the ratio of their expansions is

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a
5:3
b
3:5
c
5:6
d
6:5
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detailed solution

Correct option is A

given lengths ratio is l1l2 =53   ;diameters ratio is     r1r2=21   Δt=sameα=same α=∆ll∆t as Δt=sameα=same ∆l α l substitute the given ratio ∆l1∆l2=l1l2 =53 Does not depend on radius in linear expansion

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The coefficient of linear expansion of brass and steel are ${\mathrm{\alpha }}_{1}$ and ${\alpha }_{2}$. If we take a brass rod of length ${l}_{1}$ and steel rod of length ${l}_{\mathit{2}}$ at 0oC, their difference in length $\left({l}_{2}-{l}_{1}\right)$will remain the same at all temperatures if

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