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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). |
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Answer» `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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