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
Remain at the same height
Fall at the rate of $ 1\,cm/hour$
Fall at the rate of $ 2\,cm/hour$
Go up the rate of $1\,cm/hour$
A ball whose density is $0.4 \times 10^3\,kg/m^3$ falls into water from a height of $9\,cm$ . To what depth does the ball sink ? ....... $cm$
A hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$. The volume of the remaining cylinder is $V$ and mass $M$. It is suspended by a string in a liquid of density $\rho$, where it stays vertical. The upper surface of cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is
A block of ice floats in an oil in a vessel when the ice melts, the level of oil will ..............
A rectangular box has water in it. It is being pulled to the right with an acceleration $a$. Which of the following options shows the correct shape of water surface on it ?
Write and prove Archimedes principle.