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A cylindrical block of length \( 0.4 \mathrm{~m} \) an area of cross-section \( 0.04 \mathrm{~m}^{2} \) is placed coaxially on a thin metal disc of mass \( 0.4 \mathrm{~kg} \) and of the same cross-section. The upper face of the cylinder is maintained at a constant temperature of \( 400 \mathrm{~K} \) and the initial temperature of the disc is \( 300 \mathrm{~K} \). If the thermal conductivity
\( \mathrm{P} \) of the material of the cylinder is 10 watt \( / \mathrm{m}-\mathrm{K} \) and the specific heat of the material of the disc in

W \( 600 \mathrm{~J} / \mathrm{kg}-\mathrm{K} \), how long will it take for the temperature of the disc to increase to \( 350 \mathrm{~K} \) ? Assume, for purposes of calculation, the thermal conductivity of the disc to be very high and the system to be thermally insulated except for the upper face of the cylinder.
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