Question

Three rods made of same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at $0^{\circ }C$ and ${90}^{\circ }C$, respectively. The temperature of the junction of the three rods will be

• A. ${45}^{\circ }C$
• B. ${60}^{\circ }C$
• C. ${30}^{\circ }C$
• D. ${20}^{\circ }C$

Answer 1

The correct option is B

${60}^{\circ }C$

Let ${\theta }^{\circ }$ C be the temperature at B. Let Q be the heat flowing per second from A to B on account of temperature difference by conductivity

$\therefore Q=\frac{KA(90-\theta )}{l}$ .....(i)

Where k = thermal conductivity of the rod, A = Area of cross section of the rod, l = length of the rod. By symmetry, the same will be the case for heat flow from C to B.

$\therefore$ The heat flowing per second from B to D will be

$2Q=\frac{KA(\theta -0)}{l}$ .....(i)

Dividing Eq. (ii) by Eq. (i)

$2=\frac{\theta }{90-\theta }\Rightarrow \theta ={60}^{\circ }C$