   Chapter 9, Problem 64P

Chapter
Section
Textbook Problem

Small spheres of diameter 1.00 mm fall through 20°C water with a terminal speed of 1.10 cm/s. Calculate the density of the spheres.

To determine
The density of the spheres.

Explanation
The terminal speed of the spheres is defined as vt=2r2g(ρρf)/9η and now the density of these spheres is obtained by rearranging this expression as ρs=ρw(9ηwvt/2r2g) . Spheres diameter is d=2r and its radius is given by r=r/2 .

Given info: The terminal speed of the spheres is 1.10cm/s , density of water is 1.00×103kg/m3 , diameter of the spheres is 1.00mm , acceleration due to gravity is 9.80m/s2 and viscosity of water is 1.00×103Ns/m2 .

The formula for the density of spheres is,

ρs=36ρw(ηwvt)2d2g

• ρw is density of water.
• ηw is viscosity of water.
• vt is terminal speed of the sphere.
• r is radius of the spheres.
• g is acceleration due to gravity.

Substitute 1.00×103kg/m3 for 1.00×103kg/m3 , 1

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