Question

Q An iron ball of radius 0.3 cm falls through a column of oil of density 0.94 g/cubic cm . It is found to attain a terminal velocity of 0.5 cm/s. Determine the viscosity of oil . Density of iron is 7.8 g/cubic cm.

Answer 1

$$\begin{gathered} Dearstudent, \\ Atequilibrium, \\ viscousforce+buoyantforce=weightofball \\ so, \\ 6{\mathrm{\pi \eta aV}}_{\mathrm{T}}+{\mathrm{\rho }}_{\mathrm{L}}\mathrm{Vg}=\mathrm{mg}={\mathrm{\rho }}_{\mathrm{c}}\mathrm{Vg} \\ 6{\mathrm{\pi \eta aV}}_{\mathrm{T}}=\mathrm{V}({\mathrm{p}}_{\mathrm{c}}-{\mathrm{p}}_{\mathrm{l}})\mathrm{g} \\ \eta =\frac{2}{9}\times \frac{a^2(p_c-p_l)\times g}{V_T} \\ \eta =\frac{2}{9}\times \frac{(0.3{)}^2(6.86)\times 10}{0.5} \\ \eta =2.744poise \\ Regards \end{gathered}$$