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A conducting rod of length $1 \mathrm{~m}$ has area of cross-section $10^{-3} \mathrm{~m}^2$. One end is immersed in boiling water $\left(100^{\circ} \mathrm{C}\right)$ and the other end in Ice $\left(0^{\circ} \mathrm{C}\right)$. If coefficient of thermal conductivity of rod is $96 \mathrm{cal} / \mathrm{s} . \mathrm{m}^{\circ} \mathrm{C}$ and latent heat for ice is $8 \times 10^4 \mathrm{cal} / \mathrm{kg}$ then the amount of ice which will melt in one minute is
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$7.2 \times 10^{-3} \mathrm{~kg}$
$\begin{aligned} & \mathrm{Q}=\frac{\mathrm{KA}(\Delta \theta) \mathrm{t}}{\ell}=\mathrm{mL} \\ & \mathrm{m}=\frac{\mathrm{KA}(\Delta \theta) \mathrm{t}}{\ell \mathrm{L}}=\frac{96 \times 10^{-3} \times 100 \times 60}{1 \times 8 \times 10^4} \\ & =7.2 \times 10^{-3} \mathrm{~kg}\end{aligned}$
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