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JEE MainPhysicsGravitation

A hypothetical planet has a mass 8 times that of the Earth and a radius 2 times that of the Earth. A body has a weight W on the surface of the Earth. The height above the surface of the hypothetical planet where the weight of the body will be W 2 is (where R_E is the radius of the Earth) :

Options

  1. AR_E
  2. B2R_E
  3. C4R_E
  4. D6R_E

Correct answer

B. 2R_E

Step-by-step solution

Let M_E and R_E be the mass and radius of the Earth, respectively. The acceleration due to gravity on the surface of the Earth is g_E = GM_E R_E^2 . For the hypothetical planet, mass M_p = 8M_E and radius R_p = 2R_E . The acceleration due to gravity on the surface of the planet is: g_p = G(8M_E) (2R_E)^2 = 2 GM_E R_E^2 = 2g_E The weight of the body on the Earth's surface is W = mg_E . The weight of the body on the planet's surface is W_p = mg_p = 2mg_E = 2W . The weight of the body at a height h above the planet's

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