If earth has uniform density, and radius 'R'. The value of acceleration due to gravity at distance d above the surface is same as acceleration due to gravity at distance d below the surface.

Question

If earth has uniform density, and radius 'R'. The value of acceleration due to gravity at distance d above the surface is same as acceleration due to gravity at distance d below the surface. If d = x - 1 2 R , then find x.

TestHub · Accepted Answer

g h = g . R 2 R + d 2 h = d g d = g 0 1 - d R R 2 R + d 2 = 1 - d R R 2 . R = R + d 2 R - d R 3 = R 2 + d 2 + 2 d R R - d R 3 = R 3 + R d 2 + 2 d R 2 - d R 2 - d 3 - 2 d 2 R 0 = - d 2 R + d R 2 - d 3 d 2 + d . R - R 2 = 0 d = 5 - 1 2 R ∴ x = 5

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