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An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re)
- a)h = R2e
- b)h = Re
- c)h = 2Re
- d)h = 4Re
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An artificial satellite is moving in a circular orbit around the earth...
The escape velocity from earth is given by
ve =
The orbital velocity of a satellite revolving around earth is given by
where, Me = mass of earth, Re = radius of earth, h = height of satellite from surface of earth.
By the relation GMe = gR2s
So,
Dividing equation (i) by (ii), we get
Given,
Squaring on both side, we get
or Re + h = 2Re i.e., h = Re
ve =
The orbital velocity of a satellite revolving around earth is given by
where, Me = mass of earth, Re = radius of earth, h = height of satellite from surface of earth.
By the relation GMe = gR2s
So,
Dividing equation (i) by (ii), we get
Given,
Squaring on both side, we get
or Re + h = 2Re i.e., h = Re
Most Upvoted Answer
An artificial satellite is moving in a circular orbit around the earth...
Can be determined using the following equation:
v = sqrt(G * M / r)
Where:
v = velocity of the satellite
G = gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
M = mass of the Earth (5.972 × 10^24 kg)
r = distance from the center of the Earth to the satellite (radius of the Earth + h)
Since the satellite's speed is equal to half the magnitude of the escape velocity, we can write:
v = 0.5 * sqrt(2 * G * M / R)
Where R is the radius of the Earth (6,371 km).
We need to determine the value of h.
To find the height (h), we can rearrange the equation:
0.5 * sqrt(2 * G * M / R) = sqrt(G * M / (R + h))
0.25 * (2 * G * M / R) = (G * M / (R + h))
0.5 * G * M / R = G * M / (R + h)
0.5 * R = R + h
0.5 * R - R = h
h = -0.5 * R
Therefore, the height of the satellite above the Earth is -0.5 times the radius of the Earth. This means that the satellite is located below the surface of the Earth, which is not physically possible. Thus, the given scenario is not feasible.
v = sqrt(G * M / r)
Where:
v = velocity of the satellite
G = gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
M = mass of the Earth (5.972 × 10^24 kg)
r = distance from the center of the Earth to the satellite (radius of the Earth + h)
Since the satellite's speed is equal to half the magnitude of the escape velocity, we can write:
v = 0.5 * sqrt(2 * G * M / R)
Where R is the radius of the Earth (6,371 km).
We need to determine the value of h.
To find the height (h), we can rearrange the equation:
0.5 * sqrt(2 * G * M / R) = sqrt(G * M / (R + h))
0.25 * (2 * G * M / R) = (G * M / (R + h))
0.5 * G * M / R = G * M / (R + h)
0.5 * R = R + h
0.5 * R - R = h
h = -0.5 * R
Therefore, the height of the satellite above the Earth is -0.5 times the radius of the Earth. This means that the satellite is located below the surface of the Earth, which is not physically possible. Thus, the given scenario is not feasible.
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An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re)a)h = R2eb)h = Rec)h = 2Red)h = 4ReCorrect answer is option 'B'. Can you explain this answer?
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An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re)a)h = R2eb)h = Rec)h = 2Red)h = 4ReCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re)a)h = R2eb)h = Rec)h = 2Red)h = 4ReCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re)a)h = R2eb)h = Rec)h = 2Red)h = 4ReCorrect answer is option 'B'. Can you explain this answer?.
An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re)a)h = R2eb)h = Rec)h = 2Red)h = 4ReCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re)a)h = R2eb)h = Rec)h = 2Red)h = 4ReCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re)a)h = R2eb)h = Rec)h = 2Red)h = 4ReCorrect answer is option 'B'. Can you explain this answer?.
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