The container A is constantly maintained at $1000 C$ and insulated container B initially contains ice at $00 C$ . Different rods are used to connect them. For a rod made of copper, it takes 30 minutes for the ice to melt and for a rod of steel of same cross-section taken in different experiment it takes 60 minutes ice to melt. When these rods are simultaneously connected in parallel, the ice melts in:

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answer is B.

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Detailed Solution

Q= it, Where i= heat flow rate $= \frac{Δ T}{R} = \frac{100}{R}$

$∴ Q = (\frac{100}{R_{1}}) (30) \Rightarrow R_{1} = (\frac{100}{Q}) \times 30$
Also, $∴ Q = (\frac{100}{R_{2}}) (60) \Rightarrow R_{2} = (\frac{100}{Q}) \times 60$

$Now, Q = (\frac{1}{R_{1}} + \frac{1}{R_{2}}) t_{regd}$
$∴ t_{reqd} = \frac{Q}{(\frac{Q}{100}) \times \frac{1}{30} + (\frac{Q}{100}) \times \frac{1}{60}} = 20 m i n$