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

Given:

Two objects are at a certain distance between them.

To do:

To find out how the force of gravitation between two objects changes when the distance between them is reduced to half.

Solution:

To determine the force of gravitation between the two objects, let us know the formula used for force of gravitation first:

Formula for the force of gravitation:

Gravitational force $\boxed{F=G\frac{m_1m_2}{r^2}}$

Here, $m_1\rightarrow$ mass of first object

$m_2\rightarrow$ mass of the second object

$r\rightarrow$distance between the two object

$G\rightarrow$ A gravitational constant

When the distance between the two objects is halved

When the distance between the two objects is reduced to half,

then the distance between the objects $r'=\frac{r}{2}$

Then, gravitational force, $F'=G\frac{m_1m_2}{(r')^2}$

Or $F'=G\frac{m_1m_2}{(\frac{r}{2})^2}$

Or $F'=4\times G\frac{m_1m_2}{r^2}$

Or $F'=4F$

Thus, if the distance between the two objects is halved, the

gravitational force becomes four times.

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Updated on: 10-Oct-2022

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