Four point masses, each of the value m, are placed at the corners of a square ABCD of side l. The moment of inertia of this system about an axis passing

To calculate the moment of inertia of a system consisting of four point masses arranged at the corners of a square, we start by visualizing the square with each side measuring l . The four point masses, each of mass m, are positioned at the corners of the square, designated as points A, B, C, and D.

To find the moment of inertia about an axis that passes through the center of the square, we need to determine the distance of each mass from this central axis. The center of the square can be identified as the midpoint of the lines connecting the midpoints of opposite sides.

Hence using the properties of geometry, the distances from the square’s center toward where the masses have been placed, to each and all of the vertices are equal in length. When a point mass is concerned with the moment of inertia, all that matters to determine it would be the square of the mass’s distance away from the rotational axis.

Since all four masses are the same, we can sum up their individual contributions to obtain the total moment of inertia. The result will be a moment of inertia that captures the mass distribution relative to the axis of rotation, so that we get the final moment of inertia for the system. Thus, the answer to the question is 2ml².

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