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 given shaped glass tube having uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity $\omega $ then

Horizontal tube of non-uniform cross-section has radius of  $0.2\,m$ and  $0.1\,m$  respectively at $P$  and  $Q$ . For streamline flow of liquid, the rate of liquid flow

The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to

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 wax candle floats vertically in a liquid of density twice that of wax. The candle burns at the rate of $4\  cm/hr$ . Then, with respect to the surface of the liquid the upper end of the candle will