The area of cross-section of the wider tube shown in figure is $800$ $cm^2$. If a mass of $12$ $ kg $ is placed on the massless piston, the difference in heights $h$ in the level of water in the two tubes is  ........ $cm$

A slender homogeneous rod of length $2L$ floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is $0.75$. The length of rod that extends out of water is : 

What is buoyant force ?

Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is $36 g $ and its density is $9 g / cm^3$. If the mass of the other is $48 g$, its density in $g / cm^3$ is

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 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 ....... $cm$