A

Step 1: Identify parameters given in the problem. The radius of the cone (r) = 2 in, height (h) = 4 in, angular velocity (\omega) = 11 rad/s, and viscosity (\mu) = 3.125 \times 10^{-7} lb.s/in².
Step 2: The torque (\tau) required to maintain rotational motion in a viscous fluid can be determined using the formula: \( \tau = 2\pi r^2 \mu \frac{\omega}{h} \).
Step 3: Substitute the known values into the equation:
\( \tau = 2\pi (2)^2 (3.125 \times 10^{-7}) \frac{11}{4} \).
Step 4: Calculate \( \tau \):
\( \tau = 2\pi (4) (3.125 \times 10^{-7}) \frac{11}{4} = 2\pi (3.125 \times 10^{-7}) (11) \approx 2.16 \times 10^{-6} lb.in. \)
Therefore, the torque required to maintain this motion is approximately 2.16 \times 10^{-6} lb.in.