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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

Let g be the acceleration due to gravity at the surface of the earth. Determine the work required to slowly lift a body of mass m from the earth's surface to a height R which is equal to the earth's radius.

Options

  1. A1 2 mgR
  2. B2mgR
  3. CmgR
  4. D1 4 mgR

Correct answer

A. 1 2 mgR

Step-by-step solution

The initial potential energy of the body at the surface of the earth is given by U_i = - GMm R The final potential energy of the body at a height h = R from the surface (i.e., at a distance 2R from the center) is U_f = - GMm R + R = - GMm 2R Since the body is lifted slowly, there is no change in its kinetic energy. The work done by the external force is equal to the change in gravitational potential energy: W = U_f - U_i W = - GMm 2R - (- GMm R ) W = GMm 2R The acceleration due to gravity at the surface of the eart

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