Answer:
280 m/s2 if gravitational acceleration upon Earth's surface is 10 m/s2
Explanation:
By Newton's law of gravity we know,
F=GMm /r2
and also you know
F = mg
where G = universal gravitational constant
M = Mass of the object 1 (Earth in this case)
m = Mass of the object 2 (any object under the gravitational attraction of Earth )
r = Distance between object 1 and object 2
g = acceleration due to gravity
F = Gravitational force acting on each body
By equating above 2 equations you can get,
mg = F= GMm /r2
mg = GMm /r2
By cancelling m from both sides
g = GM/ r2
Mind G is a constant. Lets take gravitational acceleration upon Earth's surface is 10 m/s2. You get,
10 = GM/ r2 ---------------- (A)
Lets take the gravitational acceleration upon the surface a world with seven times Earth's mass and half its radius as x (or what ever you like)
you get,
x = G(7M)/(([tex]\frac{r}{2}[/tex])2
x = 7×4 GM/r2
You know the value of GM/ r2 from (A), by substituting
x = 7×4×10 = 280 m/s2
