Question

Suppose two objects are attracting each other gravitationally. If you double the distance between them, the strength of their gravitational attraction __________.

Answer 1

Answer:

decreases by a factor of 4

Explanation:

Lets take mass of the objects are m₁ and m₂ and the distance between them at initial condition is R.

We know that attraction force between two object given as

$F=G\dfrac{m_1m_2}{R^2}$

G=Constant

If distance become 2 R

R' = 2R

$F'=G\dfrac{m_1m_2}{R'^2}$

$F'=G\dfrac{m_1m_2}{(2R)^2}$

$F'=G\dfrac{m_1m_2}{4R^2}$

$F'=\dfrac{1}{4}\times G\dfrac{m_1m_2}{R^2}$

$F'=\dfrac{F}{4}$

Therefore we can say that gravitational force will become one forth of the initial force.