Two rods- one of aluminium and the other made of steel- having initial length l1 and l2 are connected together to form a single rod of length l1 - l2- The coefficients of linear expansion for aluminium and steel are -a and -a and respectively- If the length of each rod increases by the same amount when their temperature are raised by toC- then find the ratio of length of aluminium rod to the whold rod-IIT JEE 2003

The length of each rod increases by the same amount ∴ l_a = l_s⇒ I_1α_at = l_2α_st ⇒l_2/l_1 = α_a/α_s⇒l_2/l_1 + 1 = α_a/α_s + 1 ⇒l_2 + l_1/l_1 = α_a + α_s/α_s ...

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Standard XI

Physics

Thermal Expansion

Two rods, one...

Question

Two rods, one of aluminium 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 aluminium and steel are $α_{a}$ and $α_{a}$ and 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 of length of aluminium rod to the whold rod.

(IIT JEE 2003)

α_{s} / α_{a}

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α_{a} / α_{s}

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α_{s} / (α_{a} + α_{s})

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α_{a} / (α_{a} + α_{s})

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Solution

The correct option is C $α_{s} / (α_{a} + α_{s})$
The length of each rod increases by the same amount
$∴ △ l_{a} = △ l_{s} \Rightarrow △ I_{1} α_{a} t = l_{2} α_{s} t$
$\Rightarrow \frac{l_{2}}{l_{1}} = \frac{α_{a}}{α_{s}} \Rightarrow \frac{l_{2}}{l_{1}} + 1 = \frac{α_{a}}{α_{s}} + 1$
$\Rightarrow \frac{l_{2} + l_{1}}{l_{1}} = \frac{α_{a} + α_{s}}{α_{s}} \Rightarrow \frac{l_{1}}{l_{1} + l_{2}} = \frac{α_{s}}{α_{a} + α_{s}}$

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The correct option is C αs/(αa+αs)The length of each rod increases by the same amount ∴△la=△ls⇒△I1αat=l2αst ⇒l2l1=αaαs⇒l2l1+1=αaαs+1 ⇒l2+l1l1=αa+αsαs⇒l1l1+l2=αsαa+αs