Viscosity of Shampoo

• A plastic sphere ( rp=0.95 g/cm3, R = 1 cm) is dropped into a beaker of shampoo (rs=0.80 g/cm3) and sinks at a rate of 10 cm/minute.

• : What is viscosity of shampoo?

• : SF = +B + 6p R v h -W = 0

• h = (W-B)/ 6p R v

• B = Buoyant force = 4/3 p R3 rs g

• W = Weight = 4/3 p R3 rp g

• h = [2 R2 (rp - rs) g /9v] = 19.6 Pa-s

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There was a famous commercial for Prell shampoo in the early days of TV that showed a pearl slowly falling in a bottle of shampoo. I’m not sure why shampoo is supposed to be better the more viscous it is, but the commercial worked, because I still remember the name of the product after more than 40 years!

Now, all else being equal, how much faster would a pearl 2.00 cm in diameter fall through the shampoo than a pearl 1.00 cm in diameter?