Write the expression for ‘g’ on the surface of the earth of mass M and radius R.
Assume earth to be a uniform sphere.
Answers
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
)
Explanation: