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Consider a hypothetical planet whose mass and radius are both half that of Earth. If g is the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the planet will be:

Consider a hypothetical planet whose mass and radius are both half that of Earth. If g is the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the planet will be: Correct Answer 2g

  • As g = GMe / Re2

where G = Universal Gravitational Constant

Me = Mass of Earth

Re = Radius of Earth

  • Let g* be the acceleration due to gravity of the hypothetical planet mentioned in the question
  • Therefore, the acceleration due to gravity i.e g* of the hypothetical planet having mass and radius both half that of the earth will be :

g* = G x (Me/2) / (Re/2)2

g* = G x (Me/2) / (Re2/4)

= G x      2Me/(Re)2

= 2 x

= 2g (B’coz g = GMe / Re2)

  • Therefore the acceleration due to gravity (g*) of a hypothetical planet whose mass and radius are half of that of the Earth will become two times that of acceleration due to gravity of Earth (g)

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