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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

A uniform metal sphere of mass M and radius a is surrounded by a thin uniform spherical shell of equal mass and radius 4a , as shown in the figure. The centre of the shell lies on the surface of the inner sphere. Determine the gravitational field at the points P₁ and P₂ indicated in the figure.

Options

  1. AGM 16a^2 , 2GM 25a^2
  2. BGM 16a^2 , 61GM 900a^2
  3. C25GM 144a^2 , 61GM 900a^2
  4. DGM 9a^2 , 2GM 25a^2

Correct answer

B. GM 16a^2 , 61GM 900a^2

Step-by-step solution

Let the center of the spherical shell be O and the center of the inner solid sphere be C . The radius of the shell is 4a and the radius of the inner sphere is a . Since the center of the shell O lies on the surface of the inner sphere, the distance between their centers is OC = a . Consider a coordinate axis along the line passing through C , O , P₁ , and P₂ with the origin at O . From the figure, C is at a distance a above O , so the coordinate of C is +a . The bottom edge of the shell is at a distance 4a below O

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