The terminal speed attained by an aluminium sphere of radius 1 mm falling through water at 20° C will be close to (Assume laminar flow, specific gravity of A l=2.7 and η text water =8 ×-8 PI )

Question

The terminal speed attained by an aluminium sphere of radius 1 mm falling through water at 20° C will be close to (Assume laminar flow, specific gravity of A l=2.7 and η text water =8 ×-8 PI ) (A) 9.2 m/s (B) 6.9 m/s (C) 4.6 m/s (D) 2.3 m/s

Tardigrade Admin · Accepted Answer

Sepeific gravity of Al =2.7 Density of air =2.7 × 103 kg m -3 Terminal velocity v=(2 r2(ρ-σ)/9 η) =(2 ×(1 × 10-3)2(2.7 × 103-1000) × 9.8/8 × 9 × 10-4) Terminal velocity v =4.6 ms -1

Q. The terminal speed attained by an aluminium sphere of radius $1 mm$ falling through water at $2 0^{\circ} C$ will be close to (Assume laminar flow, specific gravity of $A l = 2.7$ and $η_{water} = 8 \times^{- 8} P I$ )

9.2 m/s

6.9 m/s

4.6 m/s

2.3 m/s

Sepeific gravity of Al $= 2.7$
Density of air $= 2.7 \times 1 0^{3} k g m^{- 3}$
Terminal velocity $v = \frac{2 r ^{2} ( ρ - σ )}{9 η}$
$= \frac{2 \times ( 1 \times 1 0 ^{- 3} ) ^{2} ( 2.7 \times 1 0 ^{3} - 1000 ) \times 9.8}{8 \times 9 \times 1 0 ^{- 4}}$
Terminal velocity $v = 4.6 m s^{- 1}$

Q. The terminal speed attained by an aluminium sphere of radius 1mm falling through water at 20∘C will be close to (Assume laminar flow, specific gravity of Al=2.7 and ηwater ​=8×−8PI )