Question

Calculate the value of acceleration due to gravity at height R above Earth’s surface in terms of g, where g is acceleration due to gravity at Earth surface and R is radius of Earth.

Answer 1

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→ Acceleration due to gravity:-

↪️ Acceleration produced in a body due to gravity. It is denoted by g.

• F=mg

i.e g = F/m

=> F= G.Me.m/(Re+h)²

=> F= GMem/(2Re)²

Here, G= gravitational constant = 6.67×10^-11N-m²/kg²

Me= 6 × 10²⁴ kg

Re= 6400 Km

now,

as we know...value of g = 9.8m/s (at surface of earth

g= GMem/Re² = 9.8m/s²

→ at R distance above surface of earth

g'= GMem/4Re²

g' = 9.8/4 = 2.45m/s²

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Answer 2

The value of acceleration due to gravity at height R above Earth’s surface in terms of g is  $\dfrac{g}{4}$ .

We need to find the value of g at height R above Earth’s surface .

We know ,

$mg' =\dfrac{GMm}{r^2}$

Here , r is the distance from the center of the earth .

Therefore , r = 2R .

$g'=\dfrac{GM}{(2R)^2}\\\\g'=\dfrac{GM}{4R^2}\\\\g'=\dfrac{g}{4}$

We know , $g=\dfrac{GM}{r^2}$ .

Hence , this is the required solution .

Learn More :

Gravitation

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