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(sqrt2-1))`
B. `(3)/(sqrt 2+1)`
C. `(1)/(sqrt3(sqrt2-1))`
D. `(1)/(sqrt2+1)`

Answer

B

Explanation

`((DeltaQ)/(Delta))_(BC)=((DeltaQ)/(Deltat))_(CA)`
`implies (kA(sqrt(2T)-T_(C)))/(a)=(kA(T_(C)-T))/(sqrt(2a))`
Solve to get
`(T_(C))/(T)=(3)/(sqrt(2)+1)`