An air bubble rises from the bottom of a lake to the surface. If its radius increases by $200 \%$ and the atmospheric pressure is equal to a water column of height $H$,then the depth of the lake is ..... $H$.

Why can liquids flow?

Liquid and gas both are fluids; distinguish between them and state which property is common between them.

The Karman line is a theoretical construct that separates the Earth's atmosphere from outer space. It is defined as the height at which the lift on an aircraft flying at the speed of a polar satellite $(8 \, km/s)$ is equal to its weight. Taking a fighter aircraft of wing area $30 \, m^2$ and mass $7500 \, kg$,the height of the Karman line above the ground will be in the range of .............. $km$. (Assume the density of air at height $h$ above the ground to be $\rho(h) = 1.2 e^{-h/10} \, kg/m^3$,where $h$ is in $km$,and the lift force to be $\frac{1}{2} \rho v^2 A$,where $v$ is the speed of the aircraft and $A$ is its wing area.)

When a soap bubble of radius $0.2 \ mm$ is charged,it experiences an outward electrostatic pressure of magnitude $\frac{\sigma^2}{2 \varepsilon_0}$,where $\sigma = 20 \ \mu C \ m^{-2}$ is the surface charge density. If the excess pressure inside the soap bubble due to the surface tension is same as this electrostatic pressure,then the surface tension of the soap solution is (Given: $\varepsilon_0 = 8.85 \times 10^{-12} \ C^2 \ N^{-1} \ m^{-2}$)

The temperature of an air bubble while rising from the bottom to the surface of a lake remains constant, but its diameter is doubled. If the pressure on the surface is $h$ meters of mercury column and the relative density of mercury is $\rho$, then the depth of the lake is: (in $\rho h$)