Three rods of same dimensions have thermal condutivity `3K,2K` and `K` They are arranged as shown in Then the temperature of the junction in steady state is
.

Options

A. `75^(@)C`
B. `200/3 @C`
C. `40^(@)c`
D. `100/3 @c`

Answer

B

Explanation

Suppose T be the temperature of junction. `H_(1)`, `H_(2)` and `H_(3)` are heat currents. Then `H_(1) = H_(2)+H_(3)`

or `(100-T)/(l//3KA) = (T-50)/(l//2KA)+(T-0)/(l//KA)` or `3(100-T)=2(T-50)+T`
Solving we get, `T=200_(@)/3C`