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

A square gate of size $1\,m \times 1\,m$ is hinged at its mid-point. A fluid of density $\rho$ fills the space to the left of the gate. The force F required to hold the gate stationary is

Water falls down a $500.0 \,m$ shaft to reach a turbine which generates electricity. ................ $m^3$ water must fall per second in order to generate $1.00 \times 10^9 \,W$ of power ? (Assume $50 \%$ efficiency of conversion and $\left.g=10 \,ms ^{-2}\right)$

An open-ended U-tube of uniform cross-sectional area contains water (density $10^3 kg m ^{-3}$ ). Initially the water level stands at $0.29 m$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 kg m ^{-3}$ is added to the left arm until its length is $0.1 m$, as shown in the schematic figure below. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is-

A manometer reads the pressure of a gas in an enclosure as shown in Figure $(a)$ When a pump removes some of the gas, the manometer reads as in Figure $(b)$ The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury.

$(a)$ Give the absolute and gauge pressure of the gas in the enclosure for cases $(a)$ and $(b)$, in units of cm of mercury.

$(b)$ How would the levels change in case $(b)$ if $13.6\; cm$ of water (immiscible with mercury) are poured into the right limb of the manometer ? (Ignore the small change in the volume of the gas).

A barometer kept in an elevator accelerating upwards with acceleration $\mathrm{a}$. Find most likely pressure inside the elevator.