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At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.
Correct answer is '1600'. Can you explain this answer?
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Verified Answer
At a point above the surface of the earth, the gravitational potential...
Let r be the distance of the given point from the centre of the earth. Then,
Gravitational potential = -GM/r = -5.12 × 107 J/kg ...... (1)
and acceleration due to gravity,g = GM/r2 = 6.4 m/s2 ...... (2)
Dividing (1) by (2), we get
r = 5.12 x 107 / 6.4 = 8 × 106 m = 8000km
Thus, height of the point from earth's surface = r - R = 8000 - 6400 = 1600 km
Most Upvoted Answer
At a point above the surface of the earth, the gravitational potential...
Given:
Gravitational potential (V) = 5.12 x 10^7 J/kg
Acceleration due to gravity (g) = 6.4 m/s^2
Mean radius of the Earth (R) = 6400 km = 6400000 m
Formula:
Gravitational potential (V) = gh, where g is the acceleration due to gravity and h is the height above the surface of the Earth.
Calculation:
Let's assume the height above the surface of the Earth as 'h'.
Using the formula, V = gh, we can rearrange it to solve for h:
h = V/g
Substituting the given values:
h = (5.12 x 10^7 J/kg) / (6.4 m/s^2)
1. Convert the given potential from J/kg to J/m by multiplying it with 1 kg/m:
V = 5.12 x 10^7 J/kg * 1 kg/m = 5.12 x 10^7 J/m
2. Divide the potential by the acceleration due to gravity to find the height:
h = 5.12 x 10^7 J/m / 6.4 m/s^2
3. Perform the division:
h = 8 x 10^6 m
4. Convert the height from meters to kilometers by dividing it by 1000:
h = 8 x 10^6 m / 1000 = 8 x 10^3 km
5. Subtract the mean radius of the Earth from the calculated height to get the height above the Earth's surface:
Height above Earth's surface = h - R = 8 x 10^3 km - 6400 km = 1600 km
Answer:
The height above the Earth's surface is 1600 km.
Gravitational potential (V) = 5.12 x 10^7 J/kg
Acceleration due to gravity (g) = 6.4 m/s^2
Mean radius of the Earth (R) = 6400 km = 6400000 m
Formula:
Gravitational potential (V) = gh, where g is the acceleration due to gravity and h is the height above the surface of the Earth.
Calculation:
Let's assume the height above the surface of the Earth as 'h'.
Using the formula, V = gh, we can rearrange it to solve for h:
h = V/g
Substituting the given values:
h = (5.12 x 10^7 J/kg) / (6.4 m/s^2)
Calculation Steps:
1. Convert the given potential from J/kg to J/m by multiplying it with 1 kg/m:
V = 5.12 x 10^7 J/kg * 1 kg/m = 5.12 x 10^7 J/m
2. Divide the potential by the acceleration due to gravity to find the height:
h = 5.12 x 10^7 J/m / 6.4 m/s^2
3. Perform the division:
h = 8 x 10^6 m
4. Convert the height from meters to kilometers by dividing it by 1000:
h = 8 x 10^6 m / 1000 = 8 x 10^3 km
5. Subtract the mean radius of the Earth from the calculated height to get the height above the Earth's surface:
Height above Earth's surface = h - R = 8 x 10^3 km - 6400 km = 1600 km
Answer:
The height above the Earth's surface is 1600 km.
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At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer?
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At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer?.
At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer?.
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At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer?, a detailed solution for At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer? has been provided alongside types of At a point above the surface of the earth, the gravitational potential is –5.12 × 107 J kg–1 and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth’s surface.Correct answer is '1600'. Can you explain this answer? theory, EduRev gives you an
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