Gravitation Question 361

Question: Two bodies of masses [M1andM2] are placed at a distanced/apart. What is the potential at the position where the gravitational field due to them is zero?

Options:

A) [Gd(M1+M2+2M1M2)]

B) [Gd(M1+M22M1M2)]

C) [Gd(2M1+M2+2M1M2)]

D) [G2d(M1+M2+2M1M2)]

Show Answer

Answer:

Correct Answer: A

Solution:

  • Let the gravitational field be zero at a point distant x from[M1] .

    [GM1x2=GM2(dx)2;xdx=M1M2] [xM2=M1dxM1]

    [x[M1+M2]=M1]

    [x=dM1M1+M2,dx=dM2M1+M2]

    Potential at this point due to both the masses will be [GM1xGM2(dx)]

    [=G[M1(M1+M2)dM1+M2(M1+M2)dM2]]

    [=Gd(M1+M2)2]

    [=Gd(M1+M2+2M1+M2)]



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