Answer
Verified
402k+ views
Hint – Critical velocity of a satellite is the constant horizontal velocity given to the satellite to keep it in a stable circular orbit.
Complete step-by-step answer:
We have to explain the critical velocity of a satellite.
So, the critical velocity is the constant horizontal velocity given to the satellite so as to put it into a stable circular orbit around the earth. It is denoted by \[{V_c}\] . It is also known as orbital speed or proper speed.
The critical velocity of a satellite is given by-
The expression for critical velocity can be obtained by:
Let us consider a satellite of mass m orbiting at height h from the surface of earth around the earth with critical velocity \[{V_c}\] .
Refer the figure shown below for better understanding-
Now, M and R are the mass and radius of the earth respectively.
Now, from the above figure we can see that the radius ‘r’ of the orbit is $r = R + h$
Now, while revolving around the earth, the necessary centripetal force for the circular motion of the satellite is provided by the gravitational attraction between the satellite and the earth.
So, Centripetal force = Gravitational force
So, we can write-
$\dfrac{{m{V_c}^2}}{r} = G.\dfrac{{M.m}}{{{r^2}}}$
We can also write the above expression in terms of critical velocity as-
\[{V_c}^2 = \dfrac{{GM}}{r}\]
Now keeping the value of r as, $r = R + h$ , we get-
\[{V_c}^2 = \dfrac{{GM}}{{R + h}}\]
$ \Rightarrow {V_c} = \sqrt {\dfrac{{GM}}{{R + h}}} $
If the satellite is orbiting very close to the earth’s surface, i.e., $h \ll R$ then h may be neglected in comparison of R, so critical velocity is given by-
${V_c} = \sqrt {\dfrac{{GM}}{R}} $
The above expression is of critical velocity of a satellite moving in a circular orbit around the earth.
We can see that the critical velocity depends on the radius of the earth, mass of the earth and gravitational constant, so we can say that critical velocity is constant.
Therefore, the constant horizontal velocity given to the satellite to keep it in a stable orbit is known as critical velocity.
Hence, the correct option is B.
Note – Whenever such types of questions appear, then first try to explain about the critical velocity, obtain its expression. Draw the figure so that it will be easier to understand, as mentioned in the solution. Also, keep in mind that critical velocity is the minimum velocity required to put a satellite into an orbit.
Complete step-by-step answer:
We have to explain the critical velocity of a satellite.
So, the critical velocity is the constant horizontal velocity given to the satellite so as to put it into a stable circular orbit around the earth. It is denoted by \[{V_c}\] . It is also known as orbital speed or proper speed.
The critical velocity of a satellite is given by-
The expression for critical velocity can be obtained by:
Let us consider a satellite of mass m orbiting at height h from the surface of earth around the earth with critical velocity \[{V_c}\] .
Refer the figure shown below for better understanding-
Now, M and R are the mass and radius of the earth respectively.
Now, from the above figure we can see that the radius ‘r’ of the orbit is $r = R + h$
Now, while revolving around the earth, the necessary centripetal force for the circular motion of the satellite is provided by the gravitational attraction between the satellite and the earth.
So, Centripetal force = Gravitational force
So, we can write-
$\dfrac{{m{V_c}^2}}{r} = G.\dfrac{{M.m}}{{{r^2}}}$
We can also write the above expression in terms of critical velocity as-
\[{V_c}^2 = \dfrac{{GM}}{r}\]
Now keeping the value of r as, $r = R + h$ , we get-
\[{V_c}^2 = \dfrac{{GM}}{{R + h}}\]
$ \Rightarrow {V_c} = \sqrt {\dfrac{{GM}}{{R + h}}} $
If the satellite is orbiting very close to the earth’s surface, i.e., $h \ll R$ then h may be neglected in comparison of R, so critical velocity is given by-
${V_c} = \sqrt {\dfrac{{GM}}{R}} $
The above expression is of critical velocity of a satellite moving in a circular orbit around the earth.
We can see that the critical velocity depends on the radius of the earth, mass of the earth and gravitational constant, so we can say that critical velocity is constant.
Therefore, the constant horizontal velocity given to the satellite to keep it in a stable orbit is known as critical velocity.
Hence, the correct option is B.
Note – Whenever such types of questions appear, then first try to explain about the critical velocity, obtain its expression. Draw the figure so that it will be easier to understand, as mentioned in the solution. Also, keep in mind that critical velocity is the minimum velocity required to put a satellite into an orbit.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE