First slide

Fluid statics

Question

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 2cm/hour then the top of the candle will

Moderate

A

Remain at the same height
B

Fall at the rate of 1cm/hour
C

Fall at the rate of 2cm/hour
D

Go up at the rate of 1cm/hour

Solution

In A be the cross-sectional area of the candle, then initially (2L)(A)d_c.g = (L)A.d_l.g ⇒ d_l = 2d_c. At any time if x be the length above the liquid and y be the length submerged in the liquid, then A(x + y)d_cg = A.yd_l.g

$\large \Rightarrow x=y\left ( \frac {d_l}{d_c}-1 \right )=y(2-1)=y$

If l be the total length of the candle then l = x + y = 2x ⇒ x = l/2
$\frac{d x}{d t} = \frac{1}{2} \frac{d l}{d t} = \frac{1}{2} (- 2) = - 1 c m / h r$

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