Question

derive an expression for acceleration due to gravity due to
1 shape,
2 altitude,
3 depth​

Answer 1

Answer:

Let M be mass of the earth, R be the radius of the earth

g

d

be gravitational acceleration at depth

′

d

′

from the earth surface

g be gravitational acceleration on the earth surfaces.

p be the density of the earth.

′

p

′

be the point inside the earth at depth

′

d

′

from earth surfaces.

∴CS−CP=d, ∴CP=R−d-----------(1) (since CS=R)

g=

R

2

GM

∴g=

R

2

G

3

4

πR

3

p

∴g=

3

4GπRp

--------------(2)

gd= acceleration due to gravity at depth

′

d

′

g

d

=

Cp

2

G×MassofthespherewithradiusCP

∴g

d

=

CP

2

G

3

4

πCP

3

ρ

∴g

d

=

3

4GπCPρ

-----------(3)

Dividing eq. (3) by eq(2)

g

g

d

=

R

CP

=

R

R−d

∴g

d

=g(1−

R

d

)

solution

Explanation:

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