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Four particles of masses m, 2m, 3m, 4m are kepr in sequence at the corners of a square of side a. The magnitude of gravitational force acting on a particle of mass m placed at the center of the square will be
Four particles of masses m, 2m, 3m , 4m are kept in square ABCD at the corners of a square of side a. a particle of mass m is placed at centre O of square. now, force exerted by A on O = Gm²/(a/√2)² = 2Gm²/a² force exerted by B on O = 2Gm²/(a/√2)² = 4Gm²/a² force exerted by C on O = 3Gm²/(a/√2)² = 6Gm²/a² force exerted by D on O = 4Gm²/(a/√2)² = 8Gm²/a² Let us consider F = 2Gm²/a² then, force exerted by A on O = F force exerted by B on O = 2F force exerted by C on O = 3F force exerted by D on O = 4F see figure , resultant force of B and D= 4F - 2F = 2F along CO and resultant force of A and C = 3F - F = 2F along DO now, net force acting on O = √{(2F)² + (2F)²} = 2√2F putting F = 2Gm²/a² so, net force acting on O = 4√2Gm²/a²
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