【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/21. The area moment of inertia of the area about x axis and y axis given as \( \mathrm{{I}_{{{x}{x}}}} \) and \( \mathrm{{I}_{{{y}{y}}}} \) . The x and y axis cross at origin, perpendicularly. So the polar moment of inertia of the area about origin is \( \begin{align*} \mathrm{{J}_{\text{origin}}} &= \mathrm{{I}_{{{x}{x}}}+{I}_{{{y}{y}}}} \end{align*} \)So the correct option is \( \mathrm{\text{(1st option)}\ \ {I}_{{{x}{x}}}+{I}_{{{y}{y}}}} \) ExplanationSince the polar moment of inertia is asked about the interesting point of x and y axis, we don't need to shift the given area moment axis. Explanation:Please refer to solution in this step.Step2/22. The power required can be expressed as\( \begin{align*} \mathrm{{P}} &= \mathrm{\text{Torque (T)}\time ... See the full answer