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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

In a certain region, the gravitational field is given by E = (5 N/kg ) i + (12 N/kg ) j . Determine the change in gravitational potential energy when a particle of mass 2 kg is taken from the origin to the point (12 m , 5 m ) .

Options

  1. A-120 J
  2. B-60 J
  3. C240 J
  4. D-240 J

Correct answer

D. -240 J

Step-by-step solution

The gravitational force on the particle is given by F = m E . Substituting the given values: F = 2(5 i + 12 j ) = 10 i + 24 j N The displacement of the particle from the origin to (12 m , 5 m ) is: r = 12 i + 5 j m The work done by the gravitational field is: W = F r = (10 i + 24 j ) (12 i + 5 j ) W = 10 12 + 24 5 = 120 + 120 = 240 J The change in gravitational potential energy is the negative of the work done by the conservative gravitational force: U = -W = -240 J

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