In what ratio will the force of attraction change when the mass of each of these bodies is tripled?

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Concept:

• Newton’s law of gravitation: According to this law- When two objects having some masses are placed at a certain distance then the gravitational force is directly proportional to the product of masses and it is inversely proportional to the square of the distance between them.

\(Gravitational\;Force = F \propto \frac{{{m_1}{m_2}}}{{{r^2}}} \Rightarrow F = G\frac{{{m_1}{m_2}}}{{{r^2}}}\)

Where G is gravitational constant, r is the distance between two masses, m1 and m2 are the masses.

Explanation:

Let the masses of two balls are m1 and m2 and they are separated by distance r

\(Gravitational\;Force = F = G\frac{{{m_1}{m_2}}}{{{r^2}}}\)

Now given that:

Mass of each balls and distance between them is doubled:

Mass of first ball (m1’) = 2 m1

Mass of second ball (m2’) = 2 m2

Distance between two balls (r’) = 2 r

\(New\;Gravitational\;Force\;\left( {F'} \right) = G\frac{{m_1'm_2'}}{{{{\left( {r'} \right)}^2}}} = G\frac{{\left( {2{m_1}} \right)\left( {2{m_2}} \right)}}{{{{\left( {2r} \right)}^2}}}\)

\( \implies F' = G\frac{{4{m_1}{m_2}}}{{4{r^2}}} = G\frac{{{m_1}{m_2}}}{{{r^2}}} = F\)

Hence, it will remain same.

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