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Q.

If mass M is split into two parts m and (M-m) which are then separated by a distance, the ratio of massMmthat maximises the gravitational force between the two parts is :

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a

1:4

b

1:2

c

1:1

d

2:1

answer is C.

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Detailed Solution

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F=Gm(M-m)r2=Gr2mM-m2For F to be maximum dFdm=0(as M and r are
constants)ddmGr2mM-m2=0 i.e., M2m=0    mM=12.

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If mass M is split into two parts m and (M-m) which are then separated by a distance, the ratio of massMmthat maximises the gravitational force between the two parts is :