In a vertical pneumatic air classifier separating agricultural grain from chaff, the aerodynamic drag balances the particle weight at terminal velocity: $m g = \frac{1}{2} C_d A \rho_a v_t^2$. If the mass of a seed is doubled ($2\times$) while retaining identical projected frontal area and drag coefficient, its terminal velocity increases by a factor of:
Options:
(A) $\sqrt{2} \approx 1.414$
(B) $2.0$
(C) $4.0$
(D) $1 / \sqrt{2}$
Answer Key:
A
Step-by-Step Solution & Explanation
From the force balance at terminal velocity:
$v_t = \sqrt{\frac{2mg}{\rho_a A C_d}}$
Therefore, $v_t \propto \sqrt{m}$. When mass $m$ is doubled, the terminal velocity increases by a factor of $\sqrt{2} \approx 1.414$.