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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

Four particles with masses m , 2m , 3m , and 4m are located at the four corners of a square of edge a . Determine the gravitational force acting on a particle of mass m positioned at the centre.

Options

  1. A2 2 , Gm^2 a^2
  2. B4 2 , Gm^2 a^2
  3. C4 , Gm^2 a^2
  4. D8 2 , Gm^2 a^2

Correct answer

B. 4 2 , Gm^2 a^2

Step-by-step solution

Let the corners of the square be A, B, C, D in cyclic order with masses m, 2m, 3m, 4m respectively. The distance of each corner from the centre O of the square is r = a 2 . The gravitational force on the mass m at the centre due to the mass at A is F_A = G m m r^2 = G m^2 r^2 directed towards A . The force due to the mass at C is F_C = G (3m) m r^2 = 3G m^2 r^2 directed towards C . Since A and C are opposite corners, the net force along the diagonal AC is F₁ = F_C - F_A = 2G m^2 r^2 directed towards C . Similarly,

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