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 $g =10\,ms ^{-2}$ ]

A container of height $10\, cm$ is filled with water. There is a hole at bottom. Find the pressure difference between points at top and bottom.

In the previous problem, if $15.0 \;cm$ of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury$= 13.6$)

$9\  kg$ 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 = $13.6 × 10^3\  kg/m^3$. 

The pressure at the bottom of a water tank is $4 P$. where $P$ is atmospheric pressure. If water is drawn out till the water level decreases by $\frac{3}{5}^{th}$ , then pressure at the bottom of the tank is .........

A $U$ tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of $10\,\, mm$ above the water level on the other side. Meanwhile the water rises by $65\,\, mm$ from its original level (see diagram). The density of the oil is ......... $kg/m^3$