The gravitational force between two objects i | vedclass

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(A) According to Newton's law of universal gravitation,the force $F$ between two objects of masses $m_1$ and $m_2$ separated by a distance $r$ is give

Vedclass · Accepted Answer

$0.25$

Vedclass · Answer

(A) According to Newton's law of universal gravitation,the force $F$ between two objects of masses $m_1$ and $m_2$ separated by a distance $r$ is given by $F = G \frac{m_1 m_2}{r^2}$.This implies that $F \propto \frac{1}{r^2}$.Let the initial force be $F_1 = 1 \ N$ at distance $r_1 = r$.When the distance is doubled,$r_2 = 2r$.The new force $F_2$ is given by the ratio: $\frac{F_2}{F_1} = \left(\frac{r_1}{r_2}\right)^2$.Substituting the values: $\frac{F_2}{1} = \left(\frac{r}{2r}\right)^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}$.Therefore,$F_2 = \frac{1}{4} \ N = 0.25 \ N$.

The gravitational force between two objects is $1 \ N$. If the distance between the two objects is doubled,what will be the new gravitational force between them (in $N$)?

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