A rod of metal X of length 50.0 cm elongates by 0.10 cm when it is heated from `0^(@)C" to "100^(@)C`. Another rod o metal Y of length 80.0 cm elongates by 0.08 cm for the same rise in temperature, A third rod of length 50 cm made by welding pieces of rods X and Y placed end to end, elongates by 0.03 cm when its temperature is raised from `0^(@)C" to "50^(@)C`.
The coefficients of linear expansion of metal X and of metal Y are in the ratio of

Options

A. `2:1`
B. `3:2`
C. `3:1`
D. `4:3`

Answer

A

Explanation

For rod `X, alpha_(x) =(Delta L)/(L Delta t) =(0.10)/(50.0xx100)=2.0xx10^(-5)" per "^(@)C`
For rod `Y, alpha_(y) =1.0xx10^(-5)" per "^(@)C`