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Two hollow spheres of same thickness are filled with ice. The ratio of their diameter is 1 : 2 and the ratio of thermal conductivities of the materials is 2 : 3. The ratio of times in which the ice gets melted in the two spheres is

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3 : 4

3 : 8

8 : 3

4 : 3

answer is A.

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Detailed Solution

$\begin{array}{l} {mL}_{ice} = \frac{KA (Δθ) t}{d} \Rightarrow \frac{4}{3} {πR}^{3} ρ \times L_{ice} = \frac{K 4 {πR}^{2} (Δθ) t}{d} \\ ∴ \frac{t_{1}}{t_{2}} = \frac{R_{1}}{R_{2}} \times \frac{K_{2}}{K_{1}} \end{array}$

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