$A$ cubical block of steel of each side equal to $l$ is floating on mercury in a vessel. The densities of steel and mercury are $\rho_s$ and $\rho_m$. The height of the block above the mercury level is given by:

$A$ pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. $A$ container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it is balanced. $A$ brass weight on the end of a string is then lowered into the water,but not allowed to rest on the bottom of the container. What happens next?

$A$ candle of diameter $d$ is floating on a liquid in a cylindrical container of diameter $D$ $(D >> d)$ as shown in the figure. If it is burning at the rate of $2 \text{ cm/hour}$,then the top of the candle will:

$A$ streamlined body falls through air from a height $h$ on the surface of a liquid. If $d$ and $D$ $(D > d)$ represent the densities of the material of the body and the liquid respectively,then the time after which the body will be instantaneously at rest is:

$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with an acceleration of $g/3$, the fraction of volume immersed in the liquid will be

$A$ body of density $\rho'$ is dropped from rest at a height $h$ into a lake of density $\rho$,where $\rho > \rho'$. Neglecting all dissipative forces,calculate the maximum depth to which the body sinks before returning to float on the surface.