The change in the value ′g′ at a height ′h′ above the surface of the earth is the same as at a depth ′d′ below the surface of earth. When both ′d′ and ′h′ are much smaller than the radius of earth, then which one of the fol lowing is correct?
d=h
d=2h
d=2h2
d=h2
A
d=2h
B
d=h
C
d=2h2
D
d=h2
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Solution
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Acceleration due to gravity at a depth 'd' from earth surface is:
gd=g(1−dR)
Acceleration due to gravity at height 'h' from earth surface is: he is very much smaller than R.
gh=g(1−2hR)
gh=gd
By solving it, d=2h.
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