2. Discuss variations in the value of earth’s gravitational acceleration due to a) change along the surface of the earth b) change along height c) change along depth
Answers
Answer:
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Explanation:
The acceleration due to gravity on the earth is given by
g=
R
2
GM
i.e.GM=R
2
g . . . . . . .( 1 )
The acceleration due to gravity at height 'h' from the surface of the earth is given by
g
h
=
(R+h)
2
GM
i.e.GM=(R+h)
2
g
h
. . . . . . ( 2 )
From ( 1 ) and ( 2 ) we have,
g
g
h
=
(R+h)
2
R
2
g
g
h
=(1−
R
2h
)
( b ) The acceleration due to gravity on the surface of the earth is given by.
g=
R
2
GM
. . . .( 1 )
let 'Q' be the density of the material of the earth.
Now, mass = volume × density
M=
3
4
πR
3
×ρ
Substituting in equation ( 1 ) we get
g=
R
2
G
×
3
4
πR
3
×ρ=
3
4
πGRρ
g=
3
4
πGRρ . . .. .. ( 2 )
g
d
=
3
4
πG(R−d)ρ . . . .. .( 3 )
Dividing equation( 3 ) by ( 2 ) we get
g
g
d
=
R
R−d
=(1−
R
d
)
g
d
=g(1−
R
d
)