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

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)`