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Byju's Answer

Standard XII

Physics

Thermal Expansion

A rod of leng...

Question

A rod of length 20 cm is made of metal. It expands by 0.075 cm when its temperature is raised from $0^{\circ} C$ to $100^{\circ} C$ . Another rod of a different metal B having the same length expands by 0.045 cm for the same change in temperature. A third rod of the same length is composed of two parts, one of metal A and the other of metal B. This rod expands by 0.060 cm for the same change in temperature. The portion made of metal A has the length :

20 cm

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10 cm

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15 cm

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18 cm

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Solution

The correct option is B 10 cm
Let $l_{1}$ be the length of potion of metal A and $l_{2}$ be the length of portion of metal B.
Thus $l_{1} + l_{2} = 20 c m$
For the given change in temperature, change in length $\propto$ intial length of rod.
Hence $Δ l_{1} = 0.075 \frac{l_{1}}{20}$
And $Δ l_{2} = 0.045 \frac{l_{2}}{20}$
Thus $Δ l_{1} + Δ l_{2} = 0.060$
Solving for $l_{1}$ gives
$l_{1} = 10 c m$ .

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The correct option is B 10 cmLet l1 be the length of potion of metal A and l2 be the length of portion of metal B.Thus l1+l2=20cmFor the given change in temperature, change in length ∝ intial length of rod.Hence Δl1=0.075l120And Δl2=0.045l220Thus Δl1+Δl2=0.060Solving for l1 givesl1=10cm.