Question

A mass M is broken into two parts of masses m1and m2. How are m1 and m2 related so that force of gravitational attraction between the two parts
is maximum.
(1) m1= m2
(2) m1 = 2m2
(3) m1 =9 m2
(4) m1 =M​

Answer 1

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➡️let , the masses be divided in x and (m-x)

now,

➡️F = G m. (m-x)/ r²

For, F max.. df/dx = 0

=> d/dx[G/r²(x(m-x)]

=>d/dx (mx-x²)=0

=>m.1-2x=0

=>x=m/2

➡️2nd mass= (m-x) =m/2

➡️Fmax = (G.m/2×m/2 ) / r²

➡️Gm²/4r²