If the distance between the center of two objects is quadrupled. The gravitational force between the two objects will change by a fact

Question

If the distance between the center of two objects is quadrupled. The gravitational
force between the two objects will change by a factor of:
1) 16
2) 0.25
3) 4
4) 0.0625

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Diễm Kiều 6 months 2021-07-24T19:16:44+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-07-24T19:18:10+00:00

    Answer:

    F’ = F/16

    Explanation:

    The gravitational force between masses is given by :

    F=G\dfrac{m_1m_2}{r^2}

    If the distance between the center of two objects is quadrupled, r’ = 4r

    New force will be :

    F'=G\dfrac{m_1m_2}{r'^2}\\\\F'=G\dfrac{m_1m_2}{(4r)^2}\\\\F'=\dfrac{Gm_1m_2}{16r^2}\\\\F'=\dfrac{1}{16}\times \dfrac{Gm_1m_2}{r^2}\\\\F'=\dfrac{F}{16}

    So, the new force will change by a factor of 16.

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