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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

Within the interior of a uniform spherical shell

Options

  1. Athe gravitational potential is the same everywhere
  2. Bthe gravitational field is zero
  3. Cthe gravitational potential is zero
  4. Dthe gravitational field is the same everywhere

Correct answer

D. the gravitational field is the same everywhere

Step-by-step solution

For a uniform spherical shell of mass M and radius R , the gravitational field at any point inside the shell is zero. Since the field is zero at all interior points, it is the same everywhere. The gravitational field is the negative gradient of the gravitational potential, E = - dV dr . Since E = 0 , the potential V is constant everywhere inside the shell and is equal to its value at the surface, V = - GM R . Thus, the gravitational potential is the same everywhere but not zero.

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