Karman line is a theoretical construct that separates the earth's… - Vidyadip

MCQ

Karman line is a theoretical construct that separates the earth's atmosphere from outer space. It is defined to be 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 .............. $km$ (assume the density of air at height $h$ above ground to be $\rho( h )=1.2 e ^{\frac{ h }{10}} \,kg / m ^3$ 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 $A$ its wing area).

A
$25-50$
✓
$75-100$
C
$125-150$
D
$175-200$

✓

Answer

Correct option: B.

$75-100$

b
(B)

For equilibrium :

$mg ^{\prime}=\frac{1}{2} \rho v ^2 A$

$mg \left(1-\frac{2 h }{ R }\right)=\frac{1}{2} \times 1.2 e ^{-\frac{ h }{10}} v ^2 A$

$\Rightarrow 7500 \times 9.8\left(1-\frac{2 h }{ R }\right)=0.6 e ^{-\frac{ h }{10}}\left(8 \times 10^3\right)^2 \times 30$

$\downarrow$ Neglect this term for a while and we get $h \simeq 95 \,km$

So, with $\left(1-\frac{2 h}{R}\right)$, we will get little lesser value or $h$.

$\therefore(B)$ is the answer.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 9.1 , fluid mechanics→9.1 , fluid mechanics — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A system is oscillating with undamped simple harmonic motion. Then the

A wave of frequency 100 Hz travels along a string towards its fixed end. When this wave travels back, after reflection, a node is formed at a distance of 10 cm from the fixed end. The speed of the wave (incident and reflected) is

A satellite of mass $200 \,kg$ revolves around a planet of mass $5 \times 10^{30} \,kg$ in a circular orbit of radius $6.6 \times 10^6 \,m$. Binding energy of the satellite is .............. $J$

A glass capillary tube of internal radius $r=0.25\,mm$ is immersed in water. The top end of the tube projected by $2\,cm$ above the surface of the water. At $...........^{\circ}$ angle does the liquid meet the tube.Surface tension of water $=0.7\,N / m$.

A table is revolving on its axis at $5$ revolutions per second. A sound source of frequency $1000 Hz$ is fixed on the table at $70 cm$ from the axis. The minimum frequency heard by a listener standing at a distance from the table will be .... $Hz$ (speed of sound $= 352 m/s$)

Two sound waves move in the same direction in the same medium. The pressure amplitudes of the waves are equal but the wavelength of the first wave is double the second. Let the average power transmitted across a cross-section by the first wave be P₁ and that by the 1 second wave be P₂. Then,

P₁ = P₂
P₁ = 4P₂
P₂ = 2P₁
P₂ = 4P₁

A projectile is thrown with an initial velocity of $(a \hat{ i }+b \hat{ j }) ms ^{-1}$. If the range of the projectile is twice the maximum height reached by it, then

Tangential acceleration of a particle moving in a circle of radius $1$ $m$ varies with time $t$ as (initial velocity of particle is zero). Time after which total acceleration of particle makes and angle of $30^o$ with radial acceleration is

Which of the following is not a projectile?

A particle starts oscillating simple harmonically from its equilibrium position then, the ratio of kinetic energy and potential energy of the particle at the time $T/12$ is : ($T =$ time period)