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Question
Two bodies of masses m and 4m are placed at a distance of r. Calculate the gravitational potential at a point on the line joining them where the gravitational field is zero.
Solution
Let the point be the position when the gravitational field is zero.,
`("Gm")/"x"^2 = ("G"(4"m"))/("r" - "x")^2`
`1/"x"^2 = 4/("r" - "x")^2`
Square root on both sides,
`1/"x" = 2/(("r" - "x"))`
∴ x = `"r"/3`
The point P is at a distance `"r"/3` from mass ‘m’ and `"2r"/3` from mass ‘4m’
Gravitational potential V = `(-"Gm")/(("r"/3)) - ("G"(4"m"))/(("2r"/3))`
= `(-3"Gm")/4 - (3"G"(4"m"))/(2"r")`
= `(-3"Gm")/"r" - (12"Gm")/(2"r")`
V = `(-9"Gm")/"r"`
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