How does the force of gravitation between two objects change when the distance between them is reduced to half?


Answer :

According to Universal law of gravitation, the force of attraction between two bodies is,

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

Where,

\( m_1 \ and \ m_2 \) are the masses of the two bodies.

G is the gravitational constant.

r is the distance between the two bodies.

Given if the distance is reduced to half then,

r = \( \frac{1}{2} \) r

\( \therefore F = \frac{Gm_1 m_2}{ ( \frac{r}{2} )^2 } \ \)
\(\Rightarrow \ F =4 \frac{G m_1 m_2}{r^2} \ \)
\( \Rightarrow \ F = 4 F \)

Therefore once the space between the objects is reduced to half, then the force of gravitation will increase by fourfold the first force.

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