The terminal velocity of a copper ball of radius $2.0 ext{ mm}$ falling through a tank of oil at $2

Question

The terminal velocity of a copper ball of radius $2.0	ext{ mm}$ falling through a tank of oil at $20^\circ	ext{C}$ is $6.5	ext{ cm/s}$. Compute the viscosity of the oil. (Density of oil = $1.5 	imes 10^3	ext{ kg/m}^3$, density of copper = $8.9 	imes 10^3	ext{ kg/m}^3$, $g = 9.8	ext{ m/s}^2$)

Professor PC Thomas Classes · Answer

Using Stokes' law, $v_t = \frac{2 r^2 (ho - \sigma) g}{9 \eta} \implies \eta = \frac{2 r^2 (ho - \sigma) g}{9 v_t}$. $\eta = \frac{2 	imes (2 	imes 10^{-3})^2 	imes (8.9 - 1.5) 	imes 10^3 	imes 9.8}{9 	imes 6.5 	imes 10^{-2}} \approx 0.99	ext{ Pa s}$.