at which height from the earth surface does the acceleration due to gravity decrease by 75% of it's value ar earth surface ?
Answers
If the acceleration due to gravity at some height decreases by 75% of it's value at earth surface then the height from the surface of earth is 6400 km.
Explanation:
We know the formula for the variation of acceleration of gravity with height is given by,
gh = g [1 + h/R]⁻² …… (i)
where
gh = variation in acceleration due to gravity with height
g = acceleration due to gravity at the surface of the earth
h = height of the object from the surface
R = radius of the Earth = 6400 km
It is also given that acceleration due to gravity at some height decreases by 75% of its value at the earth’s surface, therefore, we have
gh = g - [75/100]g = [25/100]g = g/4
⇒ gh / g = ¼ …… (ii)
Now, substituting (ii) in (i), we get
¼ = [1 + h/R]⁻²
⇒ [1 + h/R]² = 4
Taking roots on both sides
⇒ [1+h/R] = 2
⇒ h = [2 - 1] * R
⇒ h = 1 * 6400
⇒ h = 6400 km
Thus, at the height of 6400 km the acceleration due to gravity will decrease by 75% of it's value at the earth’s surface.
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Answer:
6400 km.......********