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.)
- A$25-50$
- B$75-100$
- C$125-150$
- D$175-200$
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When an air bubble rises from the bottom of a lake to the surface,its radius is doubled. The atmospheric pressure is equal to that of a column of water of height $H$. The depth of the lake is:
$A$ motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver $n$-times the water through the same pipe in the same time,the power of the motor must be increased as follows:
DifficultTS EAMCET 2006
View SolutionExplain why:
$(a)$ To keep a piece of paper horizontal,you should blow over,not under,it.
$(b)$ When we try to close a water tap with our fingers,fast jets of water gush through the openings between our fingers.
$(c)$ The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection.
$(d)$ $A$ fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel.
$(a)$ To keep a piece of paper horizontal,you should blow over,not under,it.
$(b)$ When we try to close a water tap with our fingers,fast jets of water gush through the openings between our fingers.
$(c)$ The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection.
$(d)$ $A$ fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel.
Medium
View SolutionState 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.
$(i)$ 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.
Medium
View SolutionThe 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 ....... $m$.
Medium
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