Calculate mass from acceleration and radius

[kmh36]

Homework Statement

How do you calculate the mass of an object just from the acceleration from gravity and the radius?

Homework Equations

My thoughts were F=GM/r2, then once you find F, you can calculate mass by M=F/A
G= 6.67 x 10^11
r = 12
Acceleration = 2 m/s^2

The Attempt at a Solution

(6.67 x 10 ^-11) / 12^2 = 4.63 * 10 ^-13
M = (4.63 * 10 ^-13)/(2 m/s^2) = 2.31 ^-13 kg

 

[BvU]

Hello 10 m/s, and welcome to PF

Acceleration from gravity due to another object happens to be independent of mass. You are missing an m in your $F = {G Mm\over r^2}$ that, with $F= ma$ goes over in $a = {G M\over r^2}$.

[edit] compare gravitational acceleration at the surface of the earth:

G = 6.67E-11 N/(m/kg)²
M = 5.97E+24 kg
r = 6.37E+06 m
g = GM/r² = 9.82E+00 m/s²​

 

[kmh36]

I'm sorry, I still don't understand! What is 10 m/s?
I didn't think my equations were right, but I really don't know what to try next. I don't know the mass which is really hanging me up.

 

[BvU]

10 m/s is 36 km/h, just a corny attempt at humor.

You don't know the mass in what kind of situation ? Could you be a bit more elaborate in the problem statement ?

Apparently you have two "things", 12 m apart, and "something" accelerates with 2 m/s² ?

 

[kmh36]

Ha, that is funny!

I'm trying to calculate the mass of an imaginary planet. All I have given to me is the radius (12m) and the acceleration due to gravity on that surface (which is 2 m/s²)

 

[BvU]

Well, then you're in business! So the problem statement is:

What is the mass of a planet with radius 12 m (!?), given that the acceleration due to gravity on the surface of that planet is 2 m/s².

And you have the equation. Is it clear that GM/r² is not a force but an acceleration ?

It's a very dense planet. Just for the fun of it, calculate the density in kg/m² assuming its a sphere...

tip: work in symbols (a, G, M, r) as long as you can, until you have a final expression (a = ...) . Then check dimensions and then fill in numbers.