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Standard VII

Physics

Conduction

Two identical...

Question

Two identical conducting rods are first connected independently to two vessels, one containing water at 100 $^{o}$ C and the other containing ice at 0 $^{o}$ C. In the second case, the rods are joined end to end and connected to the same vessels. Let $q_{1}, q_{2}$ grams/sec be the rate of melting of ice in the cases respectively. The ratio $q_{1} / q_{2}$ is

1/2

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4/1

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Solution

The correct option is B 4/1
Rate of melting of ice $q \propto \frac{1}{R}$
Thermal resistance, $\frac{q_{1}}{q_{2}} = \frac{R_{2}}{R_{1}}$
Now for series connection $R_{1} = \frac{R}{2}$
For parallel connection $R_{2} = 2 R$
$\frac{q_{1}}{q_{2}} = \frac{4}{1}$

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The correct option is B 4/1Rate of melting of ice q∝1RThermal resistance,q1q2=R2R1Now for series connection R1=R2For parallel connection R2=2Rq1q2=41

The correct option is B 4/1
Rate of melting of ice $q \propto \frac{1}{R}$
Thermal resistance, $\frac{q_{1}}{q_{2}} = \frac{R_{2}}{R_{1}}$
Now for series connection $R_{1} = \frac{R}{2}$
For parallel connection $R_{2} = 2 R$
$\frac{q_{1}}{q_{2}} = \frac{4}{1}$