A brass rod of length 500 mm and diameter 3 mm is joined to a steel rod of same length and diameter at 50$℃$. If the coefficients of linear expansion of brass and steel are $2.5 imes 10^{- 5}\ ℃^{- 1}$ and $1.25 imes 10^{- 5}\ ℃^{- 1}$, then change in length of the combined rod at 200$℃$ is

Question

A brass rod of length 500 mm and diameter 3 mm is joined to a steel rod of same length and diameter at 50$℃$. If the coefficients of linear expansion of brass and steel are $2.5 	imes 10^{- 5}\ ℃^{- 1}$ and $1.25 	imes 10^{- 5}\ ℃^{- 1}$, then change in length of the combined rod at 200$℃$ is

Dr. Abubacker · Accepted Answer

(b) Change in length of brass rod
$\mathrm{\Delta}l_{B} = \ \alpha_{B}l_{B}(T_{2} - T_{1})$
= $2.5 	imes 10^{- 5} 	imes 500 	imes (200 - 50)$
= 1.875 mm
Similarly change in length of the steel rod
$\mathrm{\Delta}il_{s} = \ \alpha_{B}l_{S}(T_{2} - T_{1})$
= $1.25 	imes 10^{- 5} 	imes 500 	imes (200 - 50)$
= 0.9375 mm
Therefore, change in length of the combined rod
= $\mathrm{\Delta}l_{B} + \mathrm{\Delta}l_{S} = 1.875 + 0.9375\ $
= 2.8175 mm =2.8 mm

Explanation

Reviewed by Dr. Abubacker

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