Answer:
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.
Answer:
The planet has one-fifth of the gravitational acceleration of the Earth.
Explanation:
Newton's law of gravitational attraction between two bodies of masses [tex]m_1[/tex] and [tex]m_2[/tex] separated by a distance d gives
[tex]F = G\dfrac{m_1m_2}{d^2}[/tex] (G is a universal constant)
For any body of mass m on the Earth surface,
[tex]F = G\dfrac{Mm}{R^2}[/tex]
Here, M and R are the mass and the radius of the Earth, respectively.
But this force is the gravitational force on the body.
[tex]F = mg = G\dfrac{Mm}{R^2}[/tex]
[tex]g = G\dfrac{M}{R^2}[/tex]
For a planet with 5 times the mass of Earth and 5 times its radius,
[tex]g_p = G\dfrac{5M}{(5R)^2} = G\dfrac{M}{5R^2} = \dfrac{1}{5}G\dfrac{M}{R^2} = \dfrac{g}{5}[/tex]
Hence the planet has one-fifth of the gravitational acceleration of the Earth.
