Question

If the terminal speed of sphere $A$ $(\text{density}=19.5{\text{kg/m}}^3)$ is $0.2\text{m/s}$ in a viscous liquid $(\text{density}=1.5{\text{kg/m}}^3)$, find the terminal speed of a sphere $B$ $\text{density}=10.5{\text{kg/m}}^{-3})$ of the same size in the same liquid.

• A. $0.4\text{m/s}$
• B. $0.133\text{m/s}$
• C. $0.1\text{m/s}$
• D. $0.2\text{m/s}$

Answer 1

The correct option is C $0.1\text{m/s}$

Terminal speed of spherical body in a viscous liquid is given by
$V_T=\frac{2r^2(\rho -\sigma )g}{9\mu }$
where $\rho$ = density of substance of a body.
$\sigma$ = density of liquid.
$\mu$=viscosity of the liquid.
From given data,
$\frac{V_T\left(B\right)}{V_T\left(A\right)}=\frac{{\rho }_B-\sigma }{{\rho }_A-\sigma }$
$V_T\left(B\right)=\frac{10.5-1.5}{19.5-1.5}\times 0.2$
$=\frac{9}{18}\times 0.2=0.1\text{m/s}$