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 $2\text{cm/hour}$, then the top of the candle will :

• A. remain at the same height
• B. fall at the rate of $1\text{cm/hour}$
• C. fall at the rate of $2\text{cm/hour}$
• D. go up at the rate of $1\text{cm/hour}$

Answer 1

The correct option is B fall at the rate of $1\text{cm/hour}$

The candle floats on the water with half its length above and below water level. Let its length be $10\text{cm}$ with $5\text{cm}$, below the surface and $5\text{cm}$ above it. If its length is reduced to $8\text{cm}$. It will have $4\text{cm}$ above water surface. So we see tip going down by $1\text{cm}$. So rate of fall of tip $=1\text{cm/hour}$.