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A mass M is split into two parts m and ...

A mass M is split into two parts m and (M-m) which are then separated by certain distance. Find ratio (m/M) to maximise the gravitational force `F=(Gm(M-m))/(r^(2))` between the parts.
Here G = gravitational constant and r is the distance between m and (M-m).

Text Solution

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`F=(Gm(M-m))/(r^(2)=(G)/(r^(2))(mM-m^(2))`
For F to be maximum `(dF)/(dm)=0`
`(d)/(dm)[(G)/(r^(2))(mM-m^(2)]=0`
` rArr "" M-2m=0`
`(m)/(M)=(1)/(2)`
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