An air bubble of volume $V_0$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure $P$ above the lake. The volume of the bubble just before touching the surface will be (density of water is $\rho$):

When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $\frac{5r}{4}$. Taking the atmospheric pressure to be equal to $10 \ m$ height of water column,the depth of the lake would approximately be ....... $m$ (ignore the surface tension and the effect of temperature).

$A$ pump is used to deliver water at a certain rate through a pipe. To obtain $n$ times the water in the same time,by what factor should the velocity of water,the force of water,and the power of the pump be increased?

The human heart discharges $75 \ cc$ of blood per beat against a pressure of $10 \ cm$ of $Hg$. If the heart beats $72$ times per minute,calculate the power of the heart in $W$. (Given: density of $Hg = 13.6 \ g/cc$ and $g = 9.8 \ m/s^2$)

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.)

An air bubble rises from the bottom of a water tank of height $5 \ m$. If the initial volume of the bubble is $3 \ mm^3$, what will be its volume as it reaches the surface (in $mm^3$)? Assume that its temperature does not change. $[g=9.8 \ m \ s^{-2}, 1 \ atm=10^5 \ Pa, \text{density of water}=1 \ g/cm^3]$