A mass `M` is broken into two parts of masses `m_(1)` and `m_(2)`. How are `m_(1)` and `m_(2)` related so that force of gravitational attraction between the two parts is maximum?

A mass `M` is broken into two parts of masses `m_(1)` and `m_(2)`. How

1.	A mass `M` is broken into two parts of masses `m_(1)` and `m_(2)`. How are `m_(1)` and `m_(2)` related so that force of gravitational attraction between the two parts is maximum?
Answer» Let `m_(1) = m`, then `m_(2) = M - m`. Gravitational force of attraction between them when placed distance `r` apart will be `F = (Gm(M - m))/(r^(2))`. Differentiating it w.r.t.`m`, we get `(dF)/(dm) = (G)/(r^(2)) [m(d)/(dm) (m - m) + (M - m) (dm)/(dm)]` `= (G)/(r^(2))[m (-1) + M - m] = (G)/r^(2)(M - 2m)` If `F` is maximum, then `(dF)/(dm) = 0`, `:. (G)/(r^(2)) (m - 2m) = 0` or `M = 2m` or `m = (M)/(2)`

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A mass `M` is broken into two parts of masses `m_(1)` and `m_(2)`. How are `m_(1)` and `m_(2)` related so that force of gravitational attraction between the two parts is maximum?

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