A rod is made of three segments of equal length with different masses. The total mass of the rod is 6m. Will the moment of inertia of the rod be (i) greater about the left end, (ii) greater about the right end, or (iii) the same about both ends

Respuesta :

Answer: (iii) the same about both ends

Explanation:

The moment of inertia is the sum of the square of the distance from the axis of massage and rotation of each length of the rod. The moment of inertia can be expressed as I = imiri2. The connection of the rod is the product of the moment length and distance (square), so it is the same at both ends.

The moment of inertia depends on the distribution of mass and the square of the distance from the axis.

The moment of inertia of the rod is the same about both ends. Hence, option (iii) is correct.

What is the moment of inertia?

The degree measure of the resistance of an object towards an angular acceleration about the given axis is known as the moment of inertia of an object.

Given data -

The total mass of rod is, M = 6m.

The moment of inertia is the sum of the square of the distance from the axis of massage and rotation of each length of the rod. The mathematical expression is given as,

[tex]I = M \times r^{2}[/tex]

Since the connection of the rod is the product of the moment length and distance (square), so it is the same at both ends.

Thus, we can conclude that the moment of inertia of the rod is the same about both the ends.

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