A hollow sphere of glass, whose external and internal radii are 11 cm and 9 cm respectively, is completely filled with ice at 0^oC. It is placed in a bath of boiling water (at 100^oC). Given, density of ice is 0.9 g cm^-3, latent heat of fusion of ice is 80 cal g^-1 and thermal conductivity of glass is 0.002 cal cm^-1 s^-1 ^oC^-1.Then,

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Rate of melting of ice is nearly $\frac{π}{2} {gs}^{- 1}$

Rate of melting of ice is nearly $2 {πgs}^{- 1}$

Time taken by ice to melt completely is nearly 10 min

Time taken by ice to melt completely is nearly 29.5 min

answer is A, D.

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Detailed Solution

Thermal resistance of sphere = $\frac{1}{4 πκ} [\frac{1}{a} - \frac{1}{b}]$
$\begin{array}{l} \frac{dm}{dt} \times 80 = \frac{100 - 0}{\frac{1}{4 π \times 2 \times 10^{- 3}} \times [\frac{1}{9} - \frac{1}{11}]} \\ \frac{dm}{dt} = 990 \frac{π}{2} \times 10^{- 3} \approx \frac{π}{2} 9 s^{- 1} \end{array}$
Time taken $= \frac{1}{60} \frac{\frac{4}{3} π \times 9 \times 9 \times 9 \times 0 .9}{\frac{990 π}{2} \times 10^{- 3}} \min$
= 29.4 min