An open $U$-tube contains mercury. When $13.6 \,cm$ of water is poured into one of the arms of the tube,then the mercury rise in the other arm from its initial level is ....... $cm$

Why is it difficult to cook on hills?

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. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is-

$A$ vertical $U$-tube of uniform cross-section contains water in both the arms. $A$ $10 \, cm$ glycerine column $(R.D. = 1.2)$ is added to one of the limbs. The level difference between the two free surfaces in the two limbs will be ...... $cm$.

The pressure at the sea surface is .......... $P_{a}$.

Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that the second vessel requires to fill up to a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases? If so,why do the vessels filled with water to that same height give different readings on a weighing scale?