Question

Calculate the % change in the value of g at a height just double the radius of earth.​

Answer 1

Answer:

Let, gh be the acceleration due to gravity at height h.

gx be the acceleration due to gravity at depth x.

The acceleration due to gravity on the surface of Earth is

g=R2GM

where,R is the radius o Earth,M is mass of Earth and G is gravitational constant. 

∴g∝R21 

⇒gh∝(R+h)21

Therefore

ggh=(R+h)2R2

ggh=(1+Rh)21

ggh=(1+Rh)−2

ggh=(1−R2h)

gh=g−R2gh

g−gh=R2gh

Also, the acceleration due to gravity at depth x,

gx=34Gρ(R−x)

⇒gx∝(R−x)

Therefore

ggx=RR−x

ggx=1−Rx

gx=g−Rgx

g−gx=Rgx

If the change in the value of g at height h above earth surface is the same as that at depth x i.e.

g−gh=g−gx

R2gh=Rgx

∴x=2h

Answer 2

Answer:

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