Question

# A hollow sphere of inner radius 5.1 cm and outer radius 7.0 cm floats half submerged...

A hollow sphere of inner radius 5.1 cm and outer radius 7.0 cm floats half submerged in a liquid of density 640 kg/m3. What is the mass of the sphere?
(in kg)

 A: 4.60×10-1 B: 6.11×10-1 C: 8.13×10-1 D: 1.08 E: 1.44

calculate the density of the material of which the sphere is made.
(in kg/m^3)

 A: 5.22×102 B: 7.57×102 C: 1.10×103 D: 1.59×103 E: 2.31×103

given
ri = 5.1 cm = 0.051 m

ro = 7.0 cm 0.07 m

rho_liquid = 640 kg/m^3

let m is the mass of the sphere.

volume of the sphere, V = (4/3)*pi*ro^3

(4/3)*pi*0.070^3

= 1.44*10^-3 m^3

in the equilibrium, net force acting on the sphere = 0

Fnety = 0

B - m*g = 0 (here B is buyont force)

B = m*g

rho_liquid*(V/2)*g = m*g

==> m = rho_liquid*(V/2)

= 640*1.44*10^-3/2

density of sphere = mass/effective volume

= 0.461/(4/3*pi*(ro^3 - ri^3))

= 0.461/(4/3*pi*(0.070^3 - 0.051^3))

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