A sample of a viscous fluid is tested in a cup and bob viscometer that has a cup radius of $2.1 \mathrm{~cm}$, a bob radius of $2.0 \mathrm{~cm}$, and a bob length of $5 \mathrm{~cm}$. When the cup is rotated at $10 \mathrm{rpm}$, the torque measured at the bob is $6,000 \mathrm{dyn} \mathrm{cm}$, and at $100 \mathrm{rpm}$, the torque is $15,000 \mathrm{dyn} \mathrm{cm}$.

(a) What is the viscosity of this sample?

(b) What can you conclude about the viscous properties of the sample?

(c) If the cup is rotated at $500 \mathrm{rpm}$, what will be the torque on the bob and the fluid viscosity? Clearly explain any assumptions you make to answer this question, and tell how you might check the validity of these assumptions.