The gravitational force between two objects i | vedclass

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(A) According to Newton's law of universal gravitation,$F = G \frac{m_1 m_2}{r^2}$.$(i)$ If the distance $r$ is reduced to half,i.e.,$r' = r/2$,the ne

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Force becomes $4F$ in both cases.

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(A) According to Newton's law of universal gravitation,$F = G \frac{m_1 m_2}{r^2}$.$(i)$ If the distance $r$ is reduced to half,i.e.,$r' = r/2$,the new force $F'$ is:$F' = G \frac{m_1 m_2}{(r/2)^2} = G \frac{m_1 m_2}{r^2 / 4} = 4 \left( G \frac{m_1 m_2}{r^2} \right) = 4F$.So,the force becomes $4$ times the original force.$(ii)$ If the mass of one object becomes four times,i.e.,$m_1' = 4m_1$,the new force $F''$ is:$F'' = G \frac{(4m_1) m_2}{r^2} = 4 \left( G \frac{m_1 m_2}{r^2} \right) = 4F$.So,the force becomes $4$ times the original force.

The gravitational force between two objects is $F$. How will this force change when:
$(i)$ the distance between them is reduced to half?
$(ii)$ the mass of one of the objects becomes four times?

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The gravitational force between two objects is $F$. How will this force change when:$(i)$ the distance between them is reduced to half?$(ii)$ the mass of one of the objects becomes four times?