There is no direct equation connecting Gravitational force and Specific gravity

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There is no direct equation connecting Gravitational force and Specific gravity.

1. Gravitational force is the force with which two bodies of mass m1m1 and m2m2 attract each other. If one of the bodies is earth the expression reduces to FGravity=GMemR2eFGravity=GMemRe2 where GG is Universal Gravitational Constant, MeandReMeandRe are the mass and radius of earth respectively and mm is the mass of other object. This equation can be written as first three are constants FGravity=mgNFGravity=mgN here, gg is the local due to gravity. NN, newton being the unit of force. FGravityFGravity is the weight of body.

2. Specific gravity is the ratio of the density of a substance to the density of a reference substance. For solids and liquids reference substance is water at 4?C4?C and at one atmospheric . For gases it is air at room temperature, 21?C21?C and at one atmospheric pressure.

We know that the density ρ≡mass per unit volumeρ≡mass per unit volume of the substance under test. We can therefore write

Specific Gravity=ρsampleρ H2OSpecific Gravity=ρsampleρ H2O We see that specific gravity is a dimensionless quantity as it is a ratio of two densities.

Indirectly both are related as follows Specific gravity can be computed from the expression for weights WW of sample and water, both of equal volume VV

SG=ρsampleρH2O=(msample/V)(mH2O/V)SG=ρsampleρH2O=(msample/V)(mH2O/V) =msamplemH2O=msamplemH2O Multiplying and dividing with gg =msamplemH2Ogg=msamplemH2Ogg or SG=WVsampleWVH2O