Finding smaller sphere mass from gravitational force between two spheres

[Spongemonkies]

Homework Statement

The gravitational force between two shperes is 2.50x10^-8. Their centers are 105 cm apart. The larger sphere has a mass of 8.20 kg. Find the mass of the smaller sphere.

Homework Equations

F=Gm1m2/d²

The Attempt at a Solution

F=Gm1m2/d²
d² x F=Gm1m2/d² x d²
Fd²=Gm1m2
Fd²/Gm1=Gm1m2/Gm1
Fd²/Gm1=m2

m2=((2.50x10^-8 N)(105² cm))/((6.67x10^-11 Nm²/kg²)(8.20 kg))
m2=5.04x10^5 kg

That can't be right because the missing mass is supposed to be smaller than 8.20 kg. Did I move the equation around right?

 

[chroot]

Are you mixing the units cm and m inappropriately?

- Warren

 

[Spongemonkies]

Okay, I forgot to convert cm to m.

But using d=1.05 meters, I get 50.4 kg as my answer. It's closer, but still too large.

 

[kdv]

Okay, I forgot to convert cm to m.

But using d=1.05 meters, I get 50.4 kg as my answer. It's closer, but still too large.

I agree with your result.

By "smaller" sphere they may have meant smaller in size, not necessarily smaller in mass.

 

[Spongemonkies]

So far though, we've only used mass for those problems.