Question

Newton's law of universal gravitation states that the gravitational force exened by an object on any other object anywhere in the universe by Gmm F= where G is the universal gravitational constant (6.67 x 10-11 N.m 2kg 2), ms is mass 1, m2 is mass 2, and r is the distance between the two masses (from conter to contor). If the distance between the two masses doubles, the gravitational force between the two masse O remains the same O is reduced to 1/4. O is reduced to 1/9, O doubles O quadruples.

Answer 1

Answer:

Gravitational force between the two will reduce to $(1/4)$ the original value.

Explanation:

The distance between the two objects was originally $r$. The gravitational force between the two objects would be:

$\displaystyle F = \frac{G\, m_{1}\, m_{2}}{r^{2}}$.

If the distance between the two is doubled, the new distance will become $2\, r$. The new gravitational force between the two will become:

$\begin{aligned}\frac{G\, m_{1}\, m_{2}}{(2\, r)^{2}} &= \frac{G\, m_{1}\, m_{2}}{4\, r^{2}} = \frac{1}{4}\, \left(\frac{G\, m_{1}\, m_{2}}{r^{2}}\right)\end{aligned}$.

In other words, the force between the two objects will become one-quarter of the initial value.