A metal rod `A` of length `l_(0)` expands by `Deltal` when its temperature is raised by `100^(@)C`. Another rod `B` of different metal of length `2l_(0)` expands by `Deltal//2` for same rise in temperature. `A` third rod `C` of length `3l_(0)` is made up of pieces of rods `A` and `B` placed end to end expands by `2Deltal` on heating through `100K` . The length of each portion of the composite rod is :-

Options

A. (a)`(5)/(3)l_(0) , (4)/(3)l_(0)`
B. (b)`l_(0), 2l_(0)`
C. (c)`(3l_(0))/(2) , (3l_(0))/(2)`
D. (d)`(2)/(3)l_(0),(7)/(3)l_(0)`

Answer

A

Explanation

For rod `A` `Deltal = l_(0)alpha_(A)(100)`
For rod `B` `(Deltal)/(2) = 2l_(0)alpha_(B)(100)`
For rod C `2Deltal = "x"alpha_(A)(100)+ (3l_(0) - "x")alpha_(B)(100)`
`implies "x" = (5)/(3) l_(0)` & `3l_(0)- "x" = (4)/(3) l_(0)`