Q. The terminal speed of a sphere of gold $(density = 19.5\ kg\ \ m^{- 3})$ is $0.2\ {ms}^{- 1}$ in a viscous liquid $(density = 1.5\ kg\ m^{- 3})$. Then the terminal speed of a sphere of silver $(density = 10.5\ kg\ m^{- 3})$ of the same size in the same liquid is
A) $0.1\ {ms}^{- 1}$
B) $1.133\ {ms}^{- 1}$
C) $0.4\ {ms}^{- 1}$
D) $0.2\ {ms}^{- 1}$
Explanation
(a) $Velocity\ \ \ \ \ v = \frac{2}{9}\ \frac{(\rho - \sigma)r^{2}g}{ɳ}$
$\therefore\ \ v \propto (\rho - \sigma)$
$\ \ \ \frac{v_{1}}{v_{2}} = \frac{(\rho_{1} - \sigma)}{(\rho_{2} - \sigma)} = 0.1m^{- 1}\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.