A hollow spherical shell at outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ $w.r.t.$ water, the value of $r$ is$……R$

A wooden piece floats half submerged in a tub of water. If the system is transferred to a lift ascending with acceleration the wooden piece will

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

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’s 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 uniform solid cylinder of density $0.8$ $g/cm^3$ floats in equilibrium in a combination of two non-mixing liquid $A$ and $B$ with its axis vertical. The densities of liquid $A$ and $B$ are $0.7$ $g/cm^3$ and $1.2$ $gm/cm^3$. The height of liquid $A$ is $h_A = 1.2$ $cm$ and the length of the part of cylinder immersed in liquid $B$ is $h_B = 0.8$ $cm$. Then the length part of the cylinder in air is ……. $cm$