The excess pressure due to surface tension in a spherical liquid drop of radius r is directly proportional to

If pressure at half the depth of a lake is equal to $2/3$ pressure at the bottom of the lake then what is the depth of the lake...... $m$

Pressure inside two soap bubbles are $1.01$ and $1.02$ atmosphere, respectively. The ratio of their volumes is

A long cylindrical glass vessel has a small hole of radius $'r'$ at its bottom. The depth to which the vessel can be lowered vertically in the deep water bath (surface tension $T$) without any water entering inside is

$Assertion :$ Smaller drops of liquid resist deforming forces better than the larger drops
$Reason :$ Excess pressure inside a drop is directly proportional to its surface area.

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be $75\, cm$ of $Hg$ and the density of water to be $1/10  $ of the density of mercury, the depth of the lake is ....... $m$