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About what axis would a uniform cube have its minimum rotational inertia? (A) Any axis passing through the center of the cube and the center of one face (B) Any axis passing through the center of the cube and the center of one edge (C) Any axis passing through the center of the cube and one vertex (a diagonal) (D) A uniform cube has the same rotational inertia for any axis of rotation through its center.

About what axis would a uniform cube have its minimum rotational inertia?
(A) Any axis passing through the center of the cube and the center of one face
(B) Any axis passing through the center of the cube and the center of one edge
(C) Any axis passing through the center of the cube and one vertex (a diagonal)
(D) A uniform cube has the same rotational inertia for any axis of rotation through its center.

Grade:upto college level

3 Answers

Navjyot Kalra
askIITians Faculty 654 Points
8 years ago
232-1392_1.PNG
The cube has minimum rotational inertia about the axis which corresponds to closer mass distribution. One can simplify the problem by considering each face of mass m , and located at its center of mass. The figure below shows the cube rotating about the given three axis of rotation: one passing of cube and center of face, one passing through center of cube and center of one edge through center, and one passing through center of cube and the center of one of vertices,

232-287_1.PNG
It can be seen from the figure above that the mass distribution is closer to the axis passing through the center of cube and one of the vertices. Therefore, the rotational inertia of the cube will be minimum for this case, and (C) will be the correct option.
Abhay
17 Points
6 years ago
(c)any axis passing through the centre of cube and one vertex Because as we consider the axis of rotation passing through the vertex (diagonal) ,the mass distributed in a uniform cube about the axis become more closer to the axis of rotation.
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

The moment of Inertia will be minimum about an axis passing through its diagonals.
This is because in this case most of the mass of the cube will lie closest to the axis of rotation which means that the moment of inertia will be least possible.

Thanks and Regards

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