At what height above the earth surface the value of g is half of its value on the earth surface .give its radius is 6000per/km
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Answer:
The height above the earth's surface = 2637 km
Explanation:
According to the law of Gravitation,
Here,
- F = Force exerted on the bodies
- G = Gravitational constant
- m = Mass of the body
- M = Mass of the Earth
- r = distance between the body and the core of the Earth.
Acceleration due to gravity,
At surface of Earth,
- r = R
- g =
Let the body be at a distance of h from the surface of the Earth and R the radius of the Earth .
- r = R + h
According to the question,
At height h,
⇒
⇒ 2R² = (R+h)²
⇒ h = (√2 - 1)R
R = 6371 km
∴ h = 2637 km
Thus,
At a height of approximately 2637 km will the acceleration due to gravity will be half of the acceleration due to gravity on the surface
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