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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

Suppose a planet in a certain solar system has a mass double the mass of the earth and a density equal to the average density of the earth. On this planet, an object that weighs W on the earth will weigh

Options

  1. A2^ 1/3 W
  2. BW/2
  3. CW
  4. D2W

Correct answer

A. 2^ 1/3 W

Step-by-step solution

The acceleration due to gravity on the surface of a planet is given by g = GM R^2 . Since the mass of the planet can be written as M = 4 3 R^3 , the acceleration due to gravity becomes g = 4 3 G R . This implies that for a constant density , the acceleration due to gravity is proportional to the radius R , so g R . Also, from M = 4 3 R^3 , we have R M^ 1/3 for a constant density. Therefore, g M^ 1/3 . Given that the mass of the planet is twice the mass of the earth ( M_p = 2M_e ) and the density is the same ( _p =

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