Question

at what height above the surface of earth the vale of acceleration due to gravity reduce by 1/8 of its value on earth??

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Answer 1

Explanation:

g=

R

2

GM

or, GM=gR

2

−(1)

Now for R→R+h [h→ height]

g

h

=

(R+h)

2

GM

or GM=(R+h)

2

g

h

−(2)

From (1) and (2)

(R+h)

2

g

h

=gR

2

or, g

h

=g(1+

R

2h

)

Similarly for R=R−d [d→ depth]

g

d

=

(R−d)

2

GM

or GM=(R−d)

2

gd −(3)

From (1) and (3)

gR

2

=(R−d)

2

gd

or g

d

=g(1−

R

d

)

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