Question

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the drawing shows two objects rotating about a vertical axis. the mass of each object is given in terms of ( m_0 ), and its perpendicular distance from the axis is given in terms of ( r_0 ). which of the following is true?

object b has a greater moment of inertia than object a.
the moments of inertia of objects a and b are equal.
object a has a greater moment of inertia than object b.

Explanation:

Step1: Calculate moment of inertia for Object A

The formula for moment of inertia \(I = mr^{2}\). For Object A, \(m = 10m_{0}\) and \(r=r_{0}\). So \(I_{A}=10m_{0}\times r_{0}^{2}\)

Step2: Calculate moment of inertia for Object B

For Object B, \(m = 2m_{0}\) and \(r = 2r_{0}\). Using \(I=mr^{2}\), we get \(I_{B}=2m_{0}\times(2r_{0})^{2}=2m_{0}\times4r_{0}^{2}=8m_{0}r_{0}^{2}\)

Answer:

Object A has a greater moment of inertia than Object B.