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Q.

A and B are two points on a uniform metal ring whose centre is C. The angle $A C B = θ$ . A and B are maintained at two different constant temperatures. When $θ = 180^{0}$ , the rate of total heat flow from A to B is 1.2 W. When $θ = 90^{0}$ , this rate will be

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a

0.9 W

b

1.6 W

c

1.8 W

d

0. 6 W

answer is C.

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Detailed Solution

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$I n f i r s t c a s e, w h e n θ = 180^{o}, e f f e c t i v e R e s i s \tan c e : R_{A B} = \frac{R}{4}$

Question Image

$\begin{array}{l} i n t h e s e c o n d c a s e : \\ w h e n θ = 90^{0}, E f f e c t i v e R e s i s \tan c e, \\ R_{A B}^{'} = \frac{\frac{3 R}{4} \times \frac{R}{4}}{R} = \frac{3 R}{16} \end{array}$

$\begin{array}{l} \frac{Q_{1}}{Q_{2}} = \frac{R_{2}}{R_{1}} = \frac{3 R}{16 \frac{R}{4}} = \frac{3}{4} \\ \Rightarrow \frac{1.2}{Q_{2}} = \frac{3}{4} \end{array}$

$\Rightarrow Q_{2} = 1.6 W$

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