Question
The earth attracts two objects $A$ and $B$ placed at same distance from its centre with same force. Prove that their masses are equal.
✓
Answer
Let mass of the body $A = m_1$ mass of the body $B = m_2$
$\text{F}_1=\frac{\text{G}\times\text{m}_\text{e}\times\text{m}_1}{\text{R}^2}$
$\text{F}_2=\frac{\text{G}\times\text{m}_\text{e}\times\text{m}_2}{\text{R}^2} m_e$ = mass of earth
As $F_1 = F_2 $
$\frac{\text{Gm}_\text{e}\text{m}_1}{\text{R}^2}=\frac{\text{Gm}_\text{e}\text{m}_2}{\text{R}^2}$
$\therefore\text{m}_1=\text{m}_2$
$\text{F}_1=\frac{\text{G}\times\text{m}_\text{e}\times\text{m}_1}{\text{R}^2}$
$\text{F}_2=\frac{\text{G}\times\text{m}_\text{e}\times\text{m}_2}{\text{R}^2} m_e$ = mass of earth
As $F_1 = F_2 $
$\frac{\text{Gm}_\text{e}\text{m}_1}{\text{R}^2}=\frac{\text{Gm}_\text{e}\text{m}_2}{\text{R}^2}$
$\therefore\text{m}_1=\text{m}_2$
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