Pressure at the bottom of a tank of water is $3P$, where $P$ is atmospheric pressure. If water is drawn out till the level of water is lowered by one fifth, then the pressure at the bottom of the tank is

Two cylindrical vessels of equal cross-sectional area $16\,cm ^{2}$ contain water upto herghts $100\,cm$ and $150\,cm$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is $......J$ [Take density of water $=10^{3}\,kg / m ^{3}$ and $g =10\,ms ^{-2}$ ]

In the figure shown, the heavy cylinder (radius $R$) resting on a smooth surface separates two liquids of densities $2\ \rho$ and $3\ \rho$ . The height $‘h’$ for the equilibrium of cylinder must be

The height of a mercury barometer is $ 75 cm$ at sea level and $ 50 cm$  at the top of a hill. Ratio of density of mercury to that of air is $10^4$. The height of the hill is ....... $km$

$9\  kg$ of mercury is poured into a glass $U-tube$ with inner diameter of $1.2 \ cm$. The mercury can flow without friction within the tube.  the oscillation period ......... $\sec$. Density of mercury = $13.6 × 10^3\  kg/m^3$. 

A air bubble rises from bottom of a lake to surface. If its radius increases by $200 \%$ and atmospheric pressure is equal to water coloumn of height $H$. then depth of lake is ..... $H$