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Gravitation

Question
CBSEENPH11020448

The change in the value of 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 following is correct?

  • d =h/2

  • d=3h/2

  • d =2h

  • d= h

Solution

C.

d =2h

fraction numerator GM over denominator left parenthesis straight R plus straight h right parenthesis squared end fraction space equals space GM over straight R cubed left parenthesis straight R minus straight d right parenthesis
rightwards double arrow space straight d space equals 2 straight h