Question

The terminal speed attained by an aluminium sphere of radius $1 mm$ falling through water at $20^{\circ} C$ will be close to (Assume laminar flow, specific gravity of $A l=2.7$ and $\eta_{\text {water }}=8 \times^{-8} PI$ )

• A. 9.2 m/s
• B. 6.9 m/s
• C. 4.6 m/s
• D. 2.3 m/s

Answer 1

Answer: (C)

Sepeific gravity of Al $=2.7$
Density of air $=2.7 \times 10^{3} \,kg\,m ^{-3}$
Terminal velocity $v=\frac{2 r^{2}(\rho-\sigma)}{9 \eta}$
$=\frac{2 \times\left(1 \times 10^{-3}\right)^{2}\left(2.7 \times 10^{3}-1000\right) \times 9.8}{8 \times 9 \times 10^{-4}}$
Terminal velocity $v =4.6\, ms ^{-1}$