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Question:

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

-6Gm/r

-9Gm/r.

zero

-4Gm/r

Solution:

Given: Two masses m and 4m kept at a distance r. Let gravitational potential be zero at a point p
Gm/x2 - G(4m)/(r-x)2 = 0
1/x = 2/(r-x)
r-x = 2x
3x = r
x = r/3
Potential at point p
V = -4Gm/(2r/3) - Gm/(r/3)
V = -6Gm/r - 3Gm/r = -9Gm/r