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 ........ $m$

Water is flowing through two horizontal pipes of different diameters which are connected together. The diameters of the two pipes are $3\, cm$ and $6\, cm$ respectively. If the speed of water in narrower pipe is $4\, m/sec$ and the pressure is $2.0\times10^4$ pascal, then the speed of water in the wider pipe is ........ $m/sec$

A boat carrying a number of large stones is floating in a water tank. What would happen to the water level if a few stones are unloaded into water

 A homogeneous solid cylinder of length $L (L < H/2)$. Cross sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure $P_0$. Then density $D$ of solid is given by

A spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta $. The time in which the velocity of the body increases from zero to $0.63\, times$ the terminal velocity $(v)$ is called time constant $\left( \tau  \right)$. Dimensionally $\tau $ can be represented by

A manometer connected to a closed tap reads $4.5\times10^5\, pascal$. When the tap is opened the reading of the manometer falls to $4\times10^5\, pascal$. Then the velocity of flow of water is ........ $ms^{-1}$