give 5 examples where there is shift from centre of the earth.
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Answer:
Given,The mass of the particle be m,
Initilly it is on the centre of the earth, so
The work done in moving a particle from center of earth to its surface W=∫
0
R
Fdr
=∫
0
R
(−
r
2
G(ρ
3
4
πr
3
)m
)dr
=∫
0
R
(−
3
4Gρπmr
)dr
=
2R
GMm
,we know that F=
R
2
GMm
=mg
=
2
1
mgR
(Since g=
R
2
GM
)
So, The work done in shifting a particle of mass from the centre of the earth to the surface of the earth is =
2
mgR
.
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