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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

Three uniform spheres, each possessing a mass M and a radius a , are positioned such that each one touches the remaining two. Determine the magnitude of the gravitational force exerted on any of the spheres by the other two.

Options

  1. A2 , GM^2 4a^2
  2. BGM^2 2a^2
  3. C3 , GM^2 a^2
  4. D3 , GM^2 4a^2

Correct answer

D. 3 , GM^2 4a^2

Step-by-step solution

The centers of the three spheres form an equilateral triangle since each sphere touches the other two. The distance between the centers of any two spheres is 2a . The gravitational force exerted by one sphere on another is given by Newton's law of gravitation: F = GM^2 (2a)^2 = GM^2 4a^2 The forces exerted on any one sphere by the other two act along the lines joining their centers, which means the angle between these two forces is 60^ . The magnitude of the resultant gravitational force is: F_ net = F^2 + F^2 + 2F

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