A hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho$. sphere is moving horizontally with an acceleration $2g,$ where $g$ is acceleration due to gravity in the space. If minimum pressure of liquid is $P_0$, then pressure at the centre of sphere is

A cylindrical vessel of base radius $R$ and height $H$ has a narrow neck of height $h$ and radius $r$ at one end (see figure). The vessel is filled with water (density $\rho_w$ ) and its neck is filled with immiscible oil (density $\rho_0$ ). Then, the pressure at

Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density $984 \;kg m^{-3}$. Determine the height (in $m$) of the wine column for normal atmospheric pressure.

At a hydroelectric power plant, the water pressure head is at a height of $300\; m$ and the water flow available is $100\; m ^{3} \,s ^{-1} .$ If the turbine generator efficiency is $60 \%,$ estimate the electric power available from the plant (in $MW$) $\left(g=9.8 \;m\,s ^{-2}\right)$

Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that the second vessel requires to fill upto a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases ? If so, why do the vessels filled with water to that same height give different readings on a weighing scale ?

Two copper vessels $A$ and $B$ have the same base area but of different shapes. $A$ takes twice the volume of water as that $B$ requires to fill upto a particular common height. Then the correct statement among the following is