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 $\rho h$)

Why is skating possible on ice?

$A$ ball is made of a material of density $\rho$ where $\rho_{\text{oil}} < \rho < \rho_{\text{water}}$,with $\rho_{\text{oil}}$ and $\rho_{\text{water}}$ representing the densities of oil and water,respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water,which of the following pictures represents its equilibrium position?

$A$ slender homogeneous rod of length $2L$ floats partly immersed in water,being supported by a string fastened to one of its ends,as shown. The specific gravity of the rod is $0.75$. The length of the rod that extends out of water is:

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.)

State whether the following statements are True or False:
$(i)$ In incompressible flow,the density of a fluid changes with time and position.
$(ii)$ Non-viscous flow can be a streamline flow.
$(iii)$ In a steady flow,the velocity of the fluid at each point remains identical with time.