If you are transported to a planet that has the same mass as Earth, but is larger in size, how would this affect your weight when standing on the planet's surface? Explain your answer.

Question

Physics

Gracie

17 November, 15:12

If you are transported to a planet that has the same mass as Earth, but is larger in size, how would this affect your weight when standing on the planet's surface? Explain your answer.

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Answers (1)

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Nigel Conrad · Answer 1

The weight will be smaller than on Earth.

Explanation:

We call weight, to the product of the mass times the acceleration produced on this mass, due to the Universal law of gravitation.

This acceleration can be obtained applying Newton's 2nd Law to the gravitational attractive force, as follows:

Fg = G m1m2 / (r12) 2 = m1 * a → a = G m2 / (r12) 2 = g

If we take a planet with the same mass, but a larger size, this means that the distance, from the planet's surface to the center, will be larger also.

As the gravitational attraction is inversely proportional to the square of the distance, this means that the acceleration caused by this force, will be smaller than on Earth.

As the mass is an universal constant, this means that the weight (as measured on a scale as the normal force) will be smaller also.