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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

Four particles, each of mass M , travel along a circle of radius R under the influence of their mutual gravitational attraction. Determine the speed of each particle.

Options

  1. AGM R ( 2 2 + 1 4 )
  2. BGM R ( 2 2 - 1 4 )
  3. CGM R ( 2 + 1 4 )
  4. DGM R ( 2 2 + 1 2 )

Correct answer

A. GM R ( 2 2 + 1 4 )

Step-by-step solution

Let the four particles be at the vertices of a square inscribed in a circle of radius R . The distance between adjacent particles is 2 R and the distance between opposite particles is 2R . The net gravitational force on any one particle towards the center of the circle is the vector sum of the forces exerted by the other three particles. The forces from the two adjacent particles are perpendicular to each other, each having a magnitude F₁ = GM^2 ( 2 R)^2 = GM^2 2R^2 . The resultant of these two forces is directed t

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