The terminal velocity of gold sphere is 39.2 cm/s
<h3>What is terminal velocity?</h3>
Terminal velocity is the maximum velocity attainable for an object as it falls through a fluid.
<h3>How to calculate the terminal velocity of the gold sphere?</h3>
The terminal velocity of the gold sphere is given by v = 2gr²(ρ - σ)/9η where
- g = acceleration due to gravity = 9.8 m/s²,
- r = radius of sphere = 100 μm = 100 × 10⁻⁶ m = 10⁻⁴ m = 10⁻² cm,
- ρ = density of sphere = 19 g/cm³,
- σ = density of water = 1.0 g/cm³ and
- η = viscosity of water = 10⁻³ Pa-s
So, susbtituting the values of the variables into the equation, we have that
v = 2gr²(ρ - σ)/9η
v = 2 × 9.8m/s²× (10⁻² cm)²(19 g/cm³ - 1.0 g/cm³)/(9 × 10⁻³ Pa-s)
v = 2 × 9.8 m/s² × 10⁻⁴ cm² × (18 g/cm³)/(9 × 10⁻³ Pa-s)
v = 2 × 980 cm/s² × 10⁻⁴ cm² × 2 g/cm³/(1 × 10⁻³ Pa-s)
v = 3920 g/s² × 10⁻⁴/(1 × 10⁻³ Pa-s)
v = 392 cm/s × 10³ × 10⁻⁴
v = 392 × 10⁻¹ cm/s
v = 39.2 cm/s
So, the terminal velocity is 39.2 cm/s
Learn more about terminal velocity of sphere here:
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