Question

Suppose you are measuring the mass of a sample using a balance that employs a standard mass of density dw = 8.0 g/ml. what is the buoyancy correction (m/m\'), if the sample density is less than 8.0 g/ml?

Answer 1

The buoyant force formula is:

$B = \rho Vg$

where $B$ is Buoyant force, $\rho$ is density, $V$ is displaced body volume and $g$ is $9.806 ms^{-2}$ (standard gravity).

The standard mass density of the sample, $\rho _{1}$ = $8 g/ml$  

If the dansity of the sample, $\rho _{2}$ $< 8 g/ml$

The buoyancy correction is determined by the ratio:

$\frac{B_{1}}{B_{2}} = \frac{\rho_{1} Vg}{\rho_{2} Vg}$

$\frac{B_{1}}{B_{2}} = \frac{\rho_{1}}{\rho_{2}}$

$\frac{B_{1}}{B_{2}} = \frac{\rho_{1}}{\rho_{2}}>1$

Hence, the the buoyancy correction is positive.