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Motion In Straight Line

Question
CBSEENPH11020315

Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

  • -4Gm/r

  • -6Gm/r

  • -9Gm/r

  • zero

Solution

C.

-9Gm/r

GM over straight x squared space equals space fraction numerator straight G left parenthesis 4 straight m right parenthesis over denominator left parenthesis straight r minus straight x squared right parenthesis end fraction
1 over straight x space equals space fraction numerator 2 over denominator straight r minus straight x end fraction
straight r minus straight x space equals space 2 straight x
3 straight x space equals space straight r over 3

= -3Gm/r - 6Gm/r = -9Gm/r