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To make a candle float stably in water in vertical orientation an aluminium cylinder of...

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To make a candle float stably in water in vertical orientation an aluminium cylinder of radius equal to that of the candle is glued at bottom of the candle Length of this cylinder is 1 0 cm and densities of wax aluminium and water are 0 8 g cm 2 7 g cm and 1 0 g cm a Find the maximum and the minimum length 1 of the candle so that it can float in water stably in vertical orientation Radius of the candle is small enough to ignore horizontal shifting of the point of application of the buoyant force b When the candle is lit it consumes wax If consumption of wax reduces length of the candle at a constant rate of 1 0 mm min and initial length of the candle is 12 0 cm how long can the candle be used for lighting always floating vertically

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