A hypothetical planet has a mass one-third of and a radius three times that of Earth. What is the acceleration due to gravity on the planet

Question

A hypothetical planet has a mass one-third of and a radius three times that of Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity on Earth?

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Vân Khánh 4 years 2021-08-25T10:34:48+00:00 1 Answers 16 views 0

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  1. phucdien
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    2021-08-25T10:36:35+00:00
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    Answer:

    Gravity of hypothetical planet is \dfrac{g}{27}.

    Explanation:

    Let the mass of Earth be ‘M’ and radius be ‘R’.

    Given:

    Mass of the hypothetical planet (m) = one-third of Earth’s mass = \frac{M}{3}

    Radius of hypothetical planet (r) = 3 times Earth’s radius = 3R

    We know that, acceleration due to gravity of a planet of mass ‘M’ and radius ‘R’ is given as:

    g=\dfrac{GM}{R^2}

    Now, the above is the value of ‘g’ for Earth.

    Now, acceleration due to gravity of hypothetical planet is given as:

    g_{hyp}=\dfrac{Gm}{r^2}\\\\g_{hyp}=\dfrac{G\times\frac{M}{3}}{(3R)^2}\\\\g_{hyp}=\dfrac{GM}{3\times 9R^2}\\\\g_{hyp}=\frac{1}{27}(\frac{GM}{R^2})=\frac{1}{27}\times g

    So, the hypothetical planet is 1/27 times of the gravity of the Earth.

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