The height ‘h’ at which the weight of a body will be the same as that of at the same depth ‘h’ from the surface of the earth is (Radius$$ of the earth is R and effect of the rotation of the earth is $$neglected):

Question

Infinity Learn · Accepted Answer

g at height  $$h=GMeRe+h2g$$ at depth  $$d=GMeRe21$$−dReFor Weight to be equal  $$GMeRe21+hRe2=GMeRe21$$−dReGiven d $$=$$ h  ⇒$$1=1+hRe21$$−hRe​⇒$$h2+hR$$−$$R2=0$$   ​comparing with $$ax2+bx+c=0a=1$$,$$b=R$$ and $$c=$$−$$R2$$​$$x=$$−b±$$b2$$−$$4ac2a$$​$$h=$$−R±$$R2$$−$$41$$−$$R221h=$$−R±$$R2+4R22$$​⇒$$h=5R$$−$$R2$$

The height ‘h’ at which the weight of a body will be the same as that of at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected):

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