Step-by-step explanation:
(b) If [tex]F_G = m_1g,[/tex] then
[tex]m_1g = G\dfrac{m_1m_2}{r^2}[/tex]
Note that [tex]m_1[/tex] cancel out so we get
[tex]g = G\dfrac{m_2}{r^2}[/tex]
Solving for [tex]m_2,[/tex] we get
[tex]m_2 = \dfrac{gr^2}{G}[/tex]
(c) I'm not sure what the problem is asking for but here goes. As r doubles, [tex]F_G[/tex] becomes
[tex]F_G = G\dfrac{m_1m_2}{(2r)^2} = \dfrac{1}{4}\left(G\dfrac{m_1m_2}{r^2}\right)[/tex]
