An 8.4-kg mass is placed at (3.0,4.0)m.Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?
A)(−3.0,−4.0)m
B)(−6.0,−8.0)m
C)(−1.5,−2.0)m
D)(1.5,2.0)m
E)There is no position giving this result.

Question

Quizplus · Accepted Answer

The moment of inertia about the z-axis for a point mass is given by $I = mr^2$, where $m$ is the mass and $r$ is the distance from the axis. To have the total moment of inertia about the z-axis be zero with two masses, one would have to negate the effect of the other. However, since the moment of inertia depends on the square of the distance, and the square of any real number is positive, it's impossible for two point masses to have a combined moment of inertia of zero about any axis. The presence of mass always contributes positively to the moment of inertia, regardless of its position relative to the axis.

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