Question

Two objects, with masses m1 and m2, are originally a distance r apart. The gravitational force between them has magnitude F. The second object has its mass changed to 2m2, and the distance is changed to r/4. What is the magnitude of the new gravitational force?
(A) 16F
(B) 32F
(C) F/16
(D) F/32

Answer 1

Answer:

The magnitude of the new gravitational force becomes 32 times of the original force.

Explanation:

Two objects, with masses m₁ and m₂, are originally a distance r apart. the gravitational force between them is given by :

$F=\dfrac{Gm_1m_2}{r^2}$

If the second object has its mass changed to 2m₂ and the distance is changed to r/4, such that,

$m_2'=2m_2$ and $r'=\dfrac{r}{4}$

The new gravitational force is given by :

$F'=G\dfrac{m_1m'_2}{r'^2}$

$F'=G\dfrac{m_1(2m_2)}{(r/4)^2}$

$F'=32\times G\dfrac{m_1m_2}{r^2}$

$F'=32F$

So, the magnitude of the new gravitational force becomes 32 times of the original force. Hence, the correct option is (B) "32F".