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∘C and 90∘C, respectively. The temperature of the junction of the three rods will be

A
45C
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B
60C
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C
30C
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D
20C
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Solution

## The correct option is B 60∘CLet θ∘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 . ∴Q=kA(90−θ)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. ∴ The heat flowing per second from B to D will be 2Q=kA(θ−0)l............(ii) Dividing Eq. (ii) by Eq. (i), we get 2=θ90−θ⇒θ=60∘C

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