Question

Suppose, two objects attract each other with a gravitationalforce of 36 Newtons. If the mass of both objects was doubledand if the distance between the objects was doubled, thenwhat would be the new force of attraction between the twoobjects?

Answer 1

EXPLANATION

Given the Newton’s Law of universal Gravitation:

$F=G\frac{m_1\cdot m_2}{r^2}$

As the force is of 36 N, we can substitute It on the function:

$F=G\frac{m_1\cdot m_2}{r^2}$

If the mass of both objects is doubled, then the force will be stronger by a factor of 4:

$F=G\frac{2m_1\cdot2m_2}{r^2}=G\frac{4m_1m_2}{r^2}$

Also, if the distance between them is doubled, then we will get a factor of 4 as shown as follows:

$F=G\frac{2m_1\cdot2m_2}{(2r)^2}=G\frac{4m_1m_2}{4r^2}$

Then, simplifying both numbers 4, we can conclude that the force will be the same:

$F=G\frac{2m_1\cdot2m_2}{(2r)^2}=G\frac{4m_1m_2}{4r^2}=G\frac{m_1m_2}{r^2}\text{ \lbrack{}Same expression\rbrack}$