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.

Explanation

Let `m_1= m" then "m_2= M-m`
Force between them when they are separated by distance 'r'
`F= (Gm(M-m))/(r^2)= (G)/(r^2)(Mm-m^2)`
For F to the maximum, differentiate R w.r.t. m and equate to zero
`(dF)/(dm)=(G)/(r^2)(M-2m)=0`
`M= 2m , m= (M)/(2)`
`M_1= m_2= (M)/(2)`.