Seven rods A, B, C, D, E, F and G are joined as shown in figure. All the rods have equal cross-sectional area A and length l. The thermal conductivies of the rods are `K_(A)=K_(C)=K_(0), `K_(B)=K_(D)=2K_(0), `K_(E)=3K_(0), `K_(F)=4K_(0)` and `K_(G)=5K_(0)` . The rod E is kept at a constant temperature `T_(1)` and the rod G is kept at a constant temperature `T_(2)(T_(2)gtT_(1))` . (a) Show that the rod F has a uniform temperature `T=(T_(1)+2T_(2))//3` . (b) Find the rate of heat flowing from the source which maintains the tempeature `T_(2)` .