Question

ce of the earth? If a planet has the same mass as the earth, but has twice the radius, how does the surface gravity, g, compare to g on the surface of the earth? It is twice as large. It is half as large. It is the same. It is four times smaller.

Answer 1

Answer:

$\large \boxed{\text{Divided by four}}$

Explanation:

The formula for gravitational force (F) is

$F = \dfrac{GmM}{d^{2} }$

where m and M are the masses of the two objects, d is the distance between their centres, and G is the gravitational constant.

If we hold m, and M constant, we can write

$F = \dfrac{k}{d^{2}}$

where k = Gmm

Thus, gravitational force is inversely proportional to the square of the distance between the objects.

 Let d₂ = the radius of the planet

And  d₁ = the radius of the Earth. Then

d₂ = 2d₁

$\dfrac{F_{2}}{F_{1}} = \dfrac{k}{d_{2}^{2}} \div \dfrac{k}{d_{1}^{2}}=\dfrac{d_{1}^{2}}{d_{2}^{2}} =\dfrac{d_{1}^{2}}{(2d_{1})^{2}} = \dfrac{1}{4}\\\\\text{If the radius of the planet is doubled, its surface gravity is \large \boxed{\textbf{divided by four}} }$