The Fg between 2 masses is 25N. If both masses are doubled and the distance is doubled (all at the same time), what is the new Fg? Use the formula: F= Gm1m2/r

Question

aum · Answer

Are you sure the formula for F is correct?  Shouldn't the denominator be r^2?

albert0898 · Answer

It should be r^2

aum · Answer

$$ \large
F_g = \frac{Gm_1m_2}{r^2}  \
25 = \frac{Gm_1m_2}{r^2} ~~ \text{ ----- (1)} \
\text{Both masses are doubled and the distance is doubled too:} \
F_g = \frac{G(2m_1)(2m_2)}{(2r)^2}  = \frac{4Gm_1m_2}{4r^2} = 
\frac{Gm_1m_2}{r^2}  = 25~\text{N  from (1)} \
$$

aum · Answer

So the force remains the same at 25 N.

albert0898 · Answer

Thank you :)