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 cone of radius $R$ and height $H$, is hanging inside a liquid of density $\rho$ by means of a string as shown in the figure. The force, due to the liquid acting on the slant surface of the cone is

A stream-lined body falls through air from a height $h$ on the surface of liquid. Let $d$ and $D$ denote the densities of the materials of the body and the liquid respectively. If  $D > d$, then the time after which the body will be instantaneously at rest, is

A concrete sphere of radius $R$  has a cavity of radius $ r$  which is packed with sawdust. The specific gravities of concrete and sawdust are respectively $2.4$  and $0.3$  for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be

A vessel contain a liquid has a constant acceleration $19.6 \,m / s ^2$ in horizontal direction. The free surface of water get sloped with horizontal at angle ……….