A 4.0-kg mass is placed at (3.0,4.0)m,and a 7.0-kg mass is placed at (3.0,−4.0)m.What is the moment of inertia of this system of masses about the x axis? A) 275 kg·m² B) 90 kg·m² C) 176 kg·m² D) 99 kg·m²

Question

Quizplus · Accepted Answer

The moment of inertia of a system of masses about an axis is given by the sum of the individual moments of inertia of each mass about that axis.

The moment of inertia of a point mass about an axis passing through its center of mass is given by:

I = mr^2

where m is the mass of the object and r is the perpendicular distance of the object from the axis of rotation.

For the 4.0-kg mass at (3.0, 4.0) m, the perpendicular distance from the x-axis is 4.0 m. So, the moment of inertia of this mass about the x-axis is:

I1 = 4.0 kg x (4.0 m)^2 = 64 kg·m^2

For the 7.0-kg mass at (3.0, -4.0) m, the perpendicular distance from the x-axis is also 4.0 m. So, the moment of inertia of this mass about the x-axis is:

I2 = 7.0 kg x (4.0 m)^2 = 112 kg·m^2

Thus, the total moment of inertia of the system about the x-axis is:

I = I1 + I2 = 64 kg·m^2 + 112 kg·m^2 = 176 kg·m^2

Therefore, the best choice is C.

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