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We know that the more force we will aplly to any object, the greater will be its density. i.e., F is directly proportional to density. On the other hand, according to universal law of force of gravitation, F=GMm/r^2. This means that F is inversely proportional to r^2. By this we can say that D is inversely proportional to r^2. On the surface r is greater than on the core or mantle. Since r is always positive, r^2 will be greatest at crust. So, the more the radius the less the density. Thus we can conclude that density is least at crust.

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