Question

A spherical ball with a radius of 2.800×10-1 m is completely submerged in a fluid that...

A spherical ball with a radius of 2.800×10-1 m is completely submerged in a fluid that has a density of 1.134×103 kg/m3.
What is the volume of the fluid displaced by the ball? (Since the ball is completely submerged, this is the same as the volume of the ball.)

What is the weight of the fluid displaced by the ball?

What is the buoyant force acting on the ball? (See Archimede's Principle in the text.)

Homework Answers

Answer #1

What is the volume of the fluid displaced by the ball?

V = (4/3) r3

where, r = 2.8 x 10-1 m

V = (4/3) (3.14) (2.8 x 10-1 m)3

V = 91.9 x 10-3 m3

V = 0.0919 m3

(b) What is the weight of the fluid displaced by the ball?

we know that, fluid = m / V m = fluid V

m = (1.134 x 103 kg/m3) (0.0919 m3)

m = 104.2 kg

(c) What is the buoyant force acting on the ball?

Fbuoyant = fluid g V

where, V = volume of the displaced fluid

g = acceleration due to gravity

fluid = density of the fluid,

then, we get

Fbuoyant = (1.134 x 103 kg/m3) (9.8 m/s2) (0.0919 m3)

Fbuoyant = 1021.3 N

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