A candle of diameter d is floating on a liquid in a cylindrical container of diameter D (D>>d) as shown in figure. If it is burning at the rate of 2 cm/hour then the top of the candle will

From Archimedes' principle, this apparent loss in weight is equal to the weight of the liquid displaced by the body.Also, volume of candle = Area x length= π(d2)2×2LWeight of candle = Weight of liquid displacedVρg = V'ρ'g'⇒(πd24×2L)ρ = (πd24×L)ρ'⇒ρρ' = 12Since candle is burning at the rate of 2 cm/h, then after an hour, candle length is 2L - 2∴ (2L-2)ρ = (L-x)ρ'∴  ρρ' = L-x2(L-1)Hence, in one hour it melts I cm and so it falls at the rate of I cm/h.