A hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho $ . sphere is moving horizontally with an acceleration $2\ g$ , 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 

Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure). Through a hole of radius $r(r < < R)$ at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is $x$. Then

A sphere of mass $M$ and radius $R$ is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

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

Two drops of equal radius are falling through air with a steady velocity of $5\,cm/s$. If the two drops coalesce, then its terminal velocity will be

A soap bubble in vacuum has a radius $3\, cm$ and another soap bubble in vacuum has radius $4\, cm$. If two bubbles coalesce under isothermal condition. Then the radius of the new bubble will be .............. $\mathrm{cm}$