Define relative density of a substance.

Is pressure a scalar or a vector? Give reason.

Consider a vessel filled with a liquid up to height $H$. The bottom of the vessel lies in the $X-Y$ plane passing through the origin. The density of the liquid varies with the $Z$-axis as $\rho(z) = \rho_0 \left[ 2 - \left( \frac{z}{H} \right)^2 \right]$. If $P_1$ and $P_2$ are the pressures at the bottom surface and top surface of the liquid respectively, the magnitude of $(P_1 - P_2)$ is:

When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $\frac{5r}{4}$. If the atmospheric pressure is equal to the pressure exerted by a $10 \ m$ height of water column,the temperature is constant,and surface tension is neglected,what is the depth of the lake (in $m$)?

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 (in $; cm$)? (Specific gravity of mercury $= 13.6$)

Why is it difficult to cook on hills?