Properties Of Solids And Liquids Question 119

Question: A rod of length 20 cm is made of metal. It expands by 0.075cm when its temperature is raised from 0°C to 100°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 [CPMT 1991]

Options:

A) 20 cm

B) 10 cm

C) 15 cm

D) 18 cm

Show Answer

Answer:

Correct Answer: B

Solution:

$ \Delta L=L _{0}\alpha \Delta \theta $

Rod A : 0.075 = 20 ´ aA ´ 100 therefore $ {\alpha _{A}}=\frac{75}{2}\times {{10}^{-6}}/{}^\circ C $

rod B : 0.045 = 20 ´ aB ´ 100 therefore $ {\alpha _{B}}=\frac{45}{2}\times {{10}^{-6}}/{}^\circ C $

For composite rod : x cm of A and (20 - x) cm of B

we have 0.060 = x aA ´ 100 + (20 - x) aB ´ 100 $ =x[ \frac{75}{2}\times {{10}^{-6}}\times 100+(20-x)\times \frac{45}{2}\times {{10}^{-6}}\times 100 ] $

On solving we get x = 10 cm.



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