Two similar rods are joined as shown in figure. Then temperature of junction is (assume no heat loss through lateral surface of rod and temperatures at the ends are shown in steady state )

Options

A. `50^(@)C`
B. `75^(@)C`
C. `66.6^(@)C`
D. `33.3^(@)C`

Answer

A

Explanation

Let `theta` be the temperature of junction.

`H_(1),H_(2),H_(3)` and `H_(4)` be the heat currents. Then and
`H_(1)=H_(2)+H_(3)+H_(4)`
or `(100-theta)/R=(theta-50)/R+(theta-50)/R+(theta-0)/R`
(R = Thermal resistance of each part of two rods)
Solving these two equations, we get
`theta= 50^(@)`C