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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

A semicircular wire possesses a mass M and a length L . A particle of mass m is positioned at the centre of the semicircle. Determine the gravitational attraction exerted on the particle by the wire.

Options

  1. A2 GMm L^2
  2. B^2 GMm L^2
  3. CGMm L^2
  4. D4 GMm L^2

Correct answer

A. 2 GMm L^2

Step-by-step solution

Let the radius of the semicircular wire be R . Since the length of the wire is L , we have L = R , which gives R = L . The linear mass density of the wire is = M L . Consider a small element of the wire of length dl subtending an angle d at the centre. The mass of this element is dM = dl = R d . The gravitational force exerted by this element on the particle of mass m at the centre is dF = G m dM R^2 = G m R d R^2 = G m R d . By symmetry, the components of the force parallel to the diameter cancel out. The net forc

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