Question

Question #c00ef

Answer 1

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

Explanation:

1. Gravitational force is the force with which two bodies of mass `m_1` and `m_2` attract each other. If one of the bodies is earth the expression reduces to
   `F_"Gravity"=G(M_e m)/R_e^2`
   where `G` is Universal Gravitational Constant, `M_e and R_e` are the mass and radius of earth respectively and `m` is the mass of other object.
   This equation can be written as first three are constants
   `F_"Gravity"=mgN`
   here, `g` is the local acceleration due to gravity.
   `N`, newton being the unit of force. `F_"Gravity"` 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^@"C"` and at one atmospheric pressure.
   For gases it is air at room temperature, `21^@"C"` and at one atmospheric pressure.

We know that the density `rho-="mass per unit volume"` of the substance under test.
We can therefore write

`"Specific Gravity" = \frac {\rho_\text{sample}}{\rho_{" H"_2"O"}}`
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 `W` of sample and water, both of equal volume `V`

`SG = \frac {\rho_\text{sample}}{\rho_(H_2O}} = \frac {(m_\text{sample}//V)}{(m_{ H_2O}//V)}`
`= \frac {m_\text{sample}}{m_{ H_2O}}`
Multiplying and dividing with `g`
`= \frac {m_\text{sample}}{m_{ H_2O}} g/g`
or `SG= \frac {W_{V_\text{sample}}}{W_{V_{ H_2O}}}`