A sphere of radius 10 cm and density 500 kg / m 3 is under water of density 1000 kg / m 3 . The acceleration of the sphere is 9.80 m / s 2 upward. Viscosity of water is 1.0 centipoise. If g = 9.81 m /

Question

A sphere of radius 10 cm and density 500 kg / m 3 is under water of density 1000 kg / m 3 . The acceleration of the sphere is 9.80 m / s 2 upward. Viscosity of water is 1.0 centipoise. If g = 9.81 m / s 2 , the velocity of the sphere is nearly

TestHub · Accepted Answer

At the stated upward acceleration, buoyancy is opposed by weight and Stokes drag:
$ρ_{f} V g - ρ_{b} V g - 6 π ηr v = ρ_{b} Va$
The printed values give:
$(1000 - 500) g \frac{4}{3} π r^{3} - 6 π ηr v = 500 \frac{4}{3} π r^{3} a$
Divide by the sphere volume and solve for speed:
$v = \frac{[( 1000 - 500 ) g - 500 a ] ( 2 r ^{2} )}{9 η}$
$r = 0.10 m, η = 0.001 Pa s, a = 9.80 m/ s^{2}$
$v = \frac{200}{18} m/s \approx 11.1 m/s$
Hence C.

Printed buoyancy, drag and weight diagram

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