A metal rod (A) of `25 cm` length expands by `0.050 cm` when its temperature is raised from `0^@ C` to `100^@ C`. Another rod (B) of a different metal of length `40 cm` expamds by `0.040 cm` for the same rise in temperature. A third rod ( C) of `50 cm` length is made up of pieces of rods (A) and (B) placed end to end expands by `0.03 cm` on heating from `0^@ C`. Find the lengths of each portion of the composite rod.

Answer

A, C, D

Explanation

From `Delta l = l prop Delta theta` we have,
`0.05 = 25 alpha_A (100)`
`:. alpha_A = 0.00002 per^@ C`
`0.04 = 40 alpha_B(100)`
`alpha_B = 0.00001 per^@ C` ,brgt In third case let (l) is the length of rod (A). Then length of rod (B) will be`(50 - l) cm`.
`Delta l = Delta l_1 + Delta l_2`
or `0.03 = l (0.00002)(50)+(50 - l)(0.00001)(50)`
Solving we get, `l = 10 cm and 50 - l = 40 cm`.