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KCET2010PhysicsGravitation

An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of earth. Which of the following could explain this?

Options

  1. ABoth the mass and radius of the planet are half as that of earth
  2. BRadius of the planet is half as that of earth, but the mass is the same as that of earth
  3. CBoth the mass and radius of the planet are twice as that of earth
  4. DMass of the planet is half as that of earth, but radius is same as that of earth

Correct answer

A. Both the mass and radius of the planet are half as that of earth

Step-by-step solution

Acceleration due to gravity on the surface of the planet is g_ p = G M_ p ² R_ p ² Given, M _ p = M _ e 2 and R _ p = R _ e 2 g_ p = G(M e / 2) ( Re / 2)² = 2 G M_ e R_ e =2 g_ e

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