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 block of steel of size $5 \times 5 \times 5 \,cm ^3$ is weighed in water. If relative density of steel is $7$ , its apparent weight is ........... $g wt$

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 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 

A spherical solid ball of volume $V$ is made of a material of density $\rho _1$ . It is falling through a liquid of density $\rho _2(\rho _2 < \rho _1)$ . Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$ , i.e., $F_{viscous} =\, -kv^2 (k > 0)$ . Then terminal speed of the ball is

A manometer reads the pressure of a gas in an enclosure as shown in the figure.

The absolute and gauge pressure of the gas in $cm$ of mercury is
(Take atmospheric pressure $= 76\,cm$ of mercury)