Question

A candle of diameter $d$ is floating on a liquid in a cylindrical container of diameter $D(D>>d)$ as shown in figure. It it is burning at the rate of $2cm/h.$ Then, the top of the candle will

• A. remain at the same height
• B. fall at the rate of $1cm/h$
• C. fall at the rate of $2cm/h$
• D. go up at the rate of $1cm/h$

Answer 1

The correct option is B fall at the rate of $1cm/h$

Since half of the candle floats up when in initial equilibrium, density of the candle is half of density of water.

Thus it always remains half inside water and half outside. Thus after an hour, the length of candle would decrease by $2cm$ and half of it would remain in water and half outside. Thus the fall in the top of the candle would be $1cm$.
Thus rate of fall of top of the candle is $1cm/h$.