3. (Chapt 14, LO 6) Consider a massless hollow sphere of unknown radius r suspen

Question

3. (Chapt 14, LO 6) Consider a massless hollow sphere of unknown radius r suspended in pure water by a mass m = 21.8 kg as shown in the figure below. The density of pure water is p 1.00 x 10 kg/m2. You may neglect the buoyant force on the mass. pure water massless hollow sphere (a) (5 pts) What is the magnitude of the gravitational force on the mass? (b) (5 pts) What is the magnitude of the buoyant force on the massless hollow sphere? (c) (5 pts) What is the radius r of the massless hollow sphere?

Explanation / Answer

(a)

gravitational force Fg = m*g

m = 21.89 kg

g = gravitational acceleration

Fg = 21.8*9.81

Fg = 214 N

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(b)

the sphere is in equilibrium

net force = 0

Fb - T =

T = tension in the string = 214 N

Fb = T

Fb = 214 N <<<<----------ANSWER

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part (c)

buoyancy force Fb = rho*V*g

rho = density of water

V = volume of sphere = (4/3)*pi*r^3

g = gravitational acceleration = 9.8 m/s^2

1.00*10^3*(4/3)*pi*r^3*9.81 = 214

radius of sphere r = 0.173 m <<<<-----ANSWER

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