why at the center of the earth gravity is zero?Explain it mathematically with example.

Asked by abinash.gupta003 | 9th Sep, 2016, 06:20: PM

Expert Answer:

Acceleration due to gravity g' at a point below the Earth at a depth 'd' is
begin mathsize 14px style straight g apostrophe equals straight g open parentheses 1 minus straight d over straight R close parentheses where space straight R space is space the space radius space of space earth apostrophe straight g apostrophe space is space the space acceleration space due space to space gravity space at space straight a space point space on space the space surface space of space earth space which space is space given space by space left parenthesis straight g space equals GM over straight R squared right parenthesis At space the space centre space of space earth space straight d space equals space straight R Therefore space colon straight g apostrophe equals straight g open parentheses 1 minus straight R over straight R close parentheses equals 0 This space shows space that space acceleration space due space to space gravity space is space zero space at space the space centre space of space earth end style

Answered by Romal Bhansali | 12th Sep, 2016, 11:14: AM

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