Question

A small metal ball of diameter $4mm$ and density $10.5g/c{m}^3$ in dropped in glycerine of density $1.5g/c{m}^3$. The ball attains a terminal velocity of $8cm/\sec$. The coefficient of viscosity of glycerine is

• A. $4.9poise$
• B. $9.8poise$
• C. $98poise$
• D. $980poise$

Answer 1

The correct option is B $9.8poise$

The terminal velocity $V_c$ of the body of radius $r$, density $\rho$ falling through a medium of density ${\rho }_o$ is given by
$V_c=\frac{2r^2(\rho -{\rho }_o)g}{9\eta }$ where $\eta$ is the coefficient of viscosity of medium.
here $r=2mm=2\times {10}^{-3}m$
$\rho =10.5g/c{m}^3=10.5\times 1000kg/m^3=10500kg/m^3$ ${\rho }_o=1.5g/c{m}^3=1500kg/m^3$
$V_T=8cm/s=0.08m/s$
$\Rightarrow 0.08=\frac{2\times (2\times {10}^{-3}{)}^2(10500-1500)\times 9.8}{9\eta }$
$\Rightarrow \eta =\frac{0.7056}{0.08\times 9}=0.98\text{decapoise}=9.8\text{poise}$