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(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)`