## has 5 times the mass of the earth and also 5 times the radius. How does the gravitational acceleration on the surface of Driff compare to th

Question

has 5 times the mass of the earth and also 5 times the radius. How does the gravitational acceleration on the surface of Driff compare to the gravitational acceleration on the surface of the earth?

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3 years 2021-08-24T02:08:10+00:00 2 Answers 11 views 0

## Answers ( )

The gravitational acceleration on earth is 5 times that on Driff.

Explanation:

The gravitational acceleration on earth is given as:

ge = Gm/r²

Where m = mass of earth, r = radius of earth.

The gravitational acceleration on Driff is given as:

gd = GM/R²

Where M = Mass of Driff, R = radius of Driff.

Since we’re told that M = 5m and R = 5r:

gd = G*5m/(5r)²

gd = Gm/5r²

Comparing this to the gravitational acceleration on earth:

ge : gd = Gm/r² : Gm/5r²

ge:gd = 5:1

The gravitational acceleration on earth is 5 times that on Driff.

The planet has one-fifth of the gravitational acceleration of the Earth.

Explanation:

Newton’s law of gravitational attraction between two bodies of masses and separated by a distance d gives

(G is a universal constant)

For any body of mass m on the Earth surface,

Here, M and R are the mass and the radius of the Earth, respectively.

But this force is the gravitational force on the body.

For a planet with 5 times the mass of Earth and 5 times its radius,

Hence the planet has one-fifth of the gravitational acceleration of the Earth.