Question

Two objects, with masses m1 and m2, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The objects are moved a distance 2r apart. The new gravitational force: A) decreases 2 times
B) increases 2 times
C) decreases 4 times D) remains unchanged
E) increases 4 times

Answer 1

Explanation:

It is given that, two objects, with masses m₁ and m₂, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. If the objects are moved a distance 2 r apart, we need to find the new gravitational force.

The gravitational force is given by :

$F=G\dfrac{m_1m_2}{r^2}$...........(1)

Let the force is F' when the objects are moved a distance 2 r apart. So,

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

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

$F'=\dfrac{1}{4}F$            (from equation (1))

So, it is clear that the magnitude of new force is F/4 i.e. decreases by a factor is 1/4. Hence, this is the required solution.