Three rods of identical area of cross-section and made from the same metal from the sides of an isosceles triangle. ABC, right angled at B. The points A and B are maintained at temperatures T and `sqrt 2T` RESPECTIVELY. In the steady state the temperature of the point C is `T_(C)`.
Assuming that only heat conduction takes place , `T_(C) / T` is equal to

Options

A. `(1)/(2(sqrt(2)-1))`
B. `(3)/(sqrt(2)+1)`
C. `(1)/(sqrt(3)(sqrt(2)-1))`
D. `(1)/(sqrt(2)+1)`

Answer

B

Explanation

`((DeltaQ)/(Deltat))_(BC)=((DeltaQ)/(Deltat))_(CA)` (for `T_(C)` to be constant)
`rArr(kA(sqrt(2)T-T_(C)))/(a)=(kA(T_(C)-T))/(sqrt(2)a)`
Solve to get: `(T_(C))/(T)=(3)/(sqrt(2)+1)`