Answer:
The variation equation is
[tex] f = \frac{k.m_1.m_2}{ {r}^{2} } [/tex]
step-by-step explanation:
From the question, the two masses are
[tex]m_1 \: and \: m_2[/tex]
This implies that the product of the two masses
[tex] = m_1 \times m_2 = m_1.m_2[/tex]
Moreover, the force,f varies directly with the products of the two masses
[tex] \implies \: f\propto m_1.m_2....eqn.1[/tex]
Also, the force varies inversely with the square of the distance,r
[tex] \implies \: f\propto \frac{1}{ {r}^{2} }.......eqn.2[/tex]
Joining equation 1 and 2, we got
[tex] \implies \: f\propto \frac{1}{ {r}^{2}} \times m_1.m_2[/tex]
[tex] \implies \: f \propto\frac{m_1.m_2}{ {r}^{2}}[/tex]
But the constant of variation is k
Multiplying the right hand side of the equation by k, we got
[tex] \implies \:f=\frac{k.m_1.m_2}{ {r}^{2}}[/tex]
