find the height of at which the weight of the body becomes half of the weight at the surface the radius is given 6400km
Answers
If the weight of the body becomes half of the weight at the surface of the Earth then the height is 2650.96 km.
Step-by-step 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 the weight of the body at height “h” becomes half of the weight at the surface, therefore, we have
gh/g = ½ …. (ii)
Now, substituting (ii) in (i), we get
1/2 = [1 – h/R]⁻²
⇒ [1-h/R]² = 2
Taking roots on both sides
⇒ [1-h/R] = √2
⇒ h = [√2 - 1] * R
⇒ h = [1.414 – 1] * 6400
⇒ h = 2650.96 km
Thus, at the height of 2650.96 km the weight of the body becomes half the weight at the surface of the earth.
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