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28 June, 17:07

In what ratio the mass 4m should be split so the value of gravitational force comes maximum for a fix distance d between the masses?

F=G (4m-x) / r^2 G/r^2 (4m-x^2)

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  1. 28 June, 17:16
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    Let mass 4m be Z

    F=G (m1 * (Z-m1) / d^2

    Using calculus ...

    dF/dm1=0=G (Z-m1) / d^2 - m1/d^2)

    solving for m1,

    Z-m1-m1=0

    m1=Z/2

    So split into 2m, and2m.

    Now if you don't know the wonderful world of calculus, then plot the following parabola, and see where it is max:

    F=G (m1 * (Z-m1) / d^2

    k=Z (m1) - (m1) ^2
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