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Grade: 11
        At what altitude in meter will the acceleration Due to gravity be 20% of that the earth`s surface (radius of Earth is R)
2 years ago

Answers : (1)

Deepak yadav
13 Points
							

Acceleration due to gravity is represented as g.
The value of g on the surface of earth is 9.8ms2

The formula for g is g=GMR2

Where G is the universal gravitational constant. Its value = 6.67408×1011m3kg1s2 .
M is the mass of earth.
R is the radius of earth.

As we see can from the formula, that g1R2 -------(1)

Lets take acceleration due to gravity at a height H from the surface as g'

g'1(R+H)2------(2)

Lets divide equation 2 with equation 1, to get the relation between g' and g

g'g=R2(R+H)2

g'=g(1+HR)2

Now that we have derived a relation between g'and g, lets solve your question by putting H=2Rin the above equation.

We get g'=g9

 acceleration due to gravity at height 2R form the surface of earth is 19th of g

Note:
The above formula is only valid for H>R.

For HR, the relation between is g' and g is

g'=g(1HR)

If the derivation is required, then feel free to ask, and I will add it.

2 years ago
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