Question

A solid square plate is spun around different axes with the same angular speed. In which of the following choice of axis of rotation will the kinetic energy of the plate be the largest?

• A. Through the central normal to the plate
• B. Along one of the diagonals of the plate
• C. Along one of the edges of the plate
• D. Through one corner normal to the plate

Answer 1

Answer: (D)

Through one corner normal to the plate

we know that rotational kinetic energy is$\frac{I{\omega }^2}{2}$.

Since $\omega$ is same for all the cases,kinetic energy will depend only upon,$I$.

Also,the largest moment of inertia of a square plate will be,when the axis passes through one corner of the plate $i.e.$ $I=\frac{7M{L}^2}{12}$,which will be the largest amongst the provided options.