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
AIIMS 2005, Medium
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The candle floats on the water with half its length above and below water level. Let its length be $10\, cm$. with $5\, cm$. below the surface and $5\, cm$. above it. If its length is reduced to $8\, cm$. It will have $4\, cm$. above water surface. So we see tip going down by $1\, cm$. So rate of fall of tip $= 1\, cm/hour$.
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A large tank is filled with water to a height $H$. A small hole is made at the base of the tank. It takes ${T_1}$ time to decrease the height of water to $\frac{H}{\eta }\,(\eta > 1)$; and it takes ${T_2}$ time to take out the rest of water. If ${T_1} = {T_2}$, then the value of $\eta $ is
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