Floating Candle
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 the bottom of the candle. Length of this cylinder is 1.00 cm and densities of wax, aluminium and water are 0.8 gm/cm^3 , 2.7 gm/cm^3 and 1.00gm/cm^3 . When the candle is lit, it consumes wax. If consumption of wax reduces length of the candle at a constant rate of 1.00 mm/ min and initial length of candle be 12.00 cm . How long the candle will light always floating vertically?
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