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On a planet, whose size is the same and mass is three times as that of the earth, find the amount of work done to lift 5   kg mass vertically upwards through 10   m on the planet. The value of g on the surface of earth is 9 . 8   m   s - 2 ​ .

Options

  1. A1 , 470   J
  2. B1 , 520   J
  3. C170   J
  4. D1 , 420   J

Correct answer

A. 1 , 470   J

Step-by-step solution

Let, M and R be the mass and radius of the earth, respectively. Then, g = G M R 2 . . . i ⁡ Now, mass of the planet, M ' = 3   m and radius of the planet, R ' = R . Let, g ' be the acceleration due to gravity on the surface of planet. Then, g ' = G M ' R ' 2 . . . ii Dividing the equations ( ii ) by ( i ) , we have g ' g = M ' M × R 2 R ' 2 = 3 M M × R 2 R 2 = 3 or g ' = 3 g = 3 × 9 . 8 = 29 . 4 m   s - 2 Now, the amount of work done to lift a m

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