SATHEE: Properties Of Solids And Liquids Question 499

Properties Of Solids And Liquids Question 499

Question: Two rods, one of aluminum and the other made of steel, having initial length $l_{1}$ and $l_{2}$ are connected together to form a single rod of length $l_{1} + l_{2}$ . The coefficients of linear expansion for aluminum and steel are $α_{a}$ and $α_{s}$ respectively. If the length of each rod increases by the same amount when their temperature are raised by $t^{o} C$ , then find the ratio $\frac{l_{1}}{(l_{1} + l_{2})}$ [IIT-JEE (Screening) 2003]

Options:

A) $\frac{α_{s}}{α_{a}}$

B) $\frac{α_{a}}{α_{s}}$

C) $\frac{α_{s}}{(α_{a} + α_{s})}$

D) $\frac{α_{a}}{(α_{a} + α_{s})}$

Show Answer

Answer:

Correct Answer: C

Solution:

Given $Δ l_{1} = Δ l_{2}$ or $l_{1} α_{a} t = l_{2} α_{s} t$

$∴$ $\frac{l_{1}}{l_{2}} = \frac{α_{s}}{α_{a}}$ or $\frac{l_{1}}{l_{1} + l_{2}} = \frac{α_{s}}{α_{a} + α_{s}}$ .

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Properties Of Solids And Liquids Question 499

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