Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is [(2√2 + 1)/32](Gm²/L²), the length of the sides of the square is
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Question

Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is [(2√2 + 1)/32](Gm²/L²), the length of the sides of the square is

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G1 Physics · Accepted Answer

For side a: F = Gm²/a² Force due to diagonal mass: F' = Gm²/(2a²) Net force: Fₙₑₜ = √2 F + F' = (Gm²/a²)(√2 + 1/2) = [(2√2 + 1)/2](Gm²/a²) Equating with the given force gives: a = 4L