Assume the density of brass weights to be 8 g ${\mathrm{cm}}^{-3}$ and that of air to be 0.0012 g ${\mathrm{cm}}^{-3}$. What fractional error arises from neglecting buoyancy of air in weighing and object of density 3.4 g ${\mathrm{cm}}^{-\mathrm{l}}$ on a beam balance?

Let m gwt the weight of object in vaccum.

Volume of object = $\frac{\mathrm{m}}{3.4}$

Weight of air displaced by object = $\frac{\mathrm{m}}{3.4}\times 0.0012$

Volume of brass weight = $\frac{\mathrm{m}}{8}$

Weight of air displaced by brass weighs = $\frac{\mathrm{m}}{8}\times 0.0012$

Error = difference in buoyance

      = m0.0012[$\frac{1}{3.4}-\frac{1}{8}$]

Fractional error = $\frac{0.0012\times 4.6}{3.4 \times 8} = 2 \times {10}^{-4}$