Correct Answer - C
Let `T_(0)` be the temperature of point C and x be the length of rod AB or BC . Then
`CA =sqrt(x^(2) + x^(2)) = sqrt(2)x`
At steady state, the rate of heat flowing from B to C = rate of heat flowing from C to A.
`:. (KA(sqrt(2)T - T_(0)))/(x) = (KA(T_(0) - T))/(sqrt(2)x)`
or `sqrt(2) (sqrt(2)T- T_(0)) = T_(0) - T`
On solving, `T_(0) = (3T)/((sqrt(2) + 1))`