A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$ The fraction of volume immersed in the liquid will be

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 

A .......... $m/s$ speed the velocity head of water is equal to pressure head of $40\, cm$ of $Hg$ .

Work of $3.0\times10^{-4}$ joule is required to be done in increasing the size of a soap film from $10\, cm\times6\, cm$ to $10\, cm\times11\, cm$. The surface tension of the film is

A homogeneous solid cylinder of length $L (L < H/2)$ , cross-sectional area $A$ 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 figure. The lower density liquid is open to atmosphere having pressure $P_0$ . Then, density $D$ of solid is given by

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