Chapter 8 Rational Functions - 8.1 Model Inverse and Joint Variation - 8.1 Exercises - Problem Solving - Page 557: 41c

$\dfrac{F(rm_1, rm_2)}{F(m_1, m_2)}=r^2$ and $\dfrac{F(rd)}{F(d)}=r^{-2}$

Work Step by Step

From the previous part (a), we have $F= G\dfrac{m_1m_2}{d^2}$ As the masses of the objects increase the force increases and the $d$ is kept constant. When each of the masses gets increased by the common ratio, then $\dfrac{F(rm_1, rm_2)}{F(m_1, m_2)}=r^2$ As the distance between the objects increases, the force decreases. When the distance gets increased by $r$, then $\dfrac{F(rd)}{F(d)}=r^{-2}$ Hence, $\dfrac{F(rm_1, rm_2)}{F(m_1, m_2)}=r^2$ and $\dfrac{F(rd)}{F(d)}=r^{-2}$

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