Question

the disk shown below in (1) clearly has its center of mass at the center. suppose the disk is cut in half and the pieces arranged as shown in (2). where is the center of mass of (2) as compared to (1)? a. higher b. lower c. the same place d. the concept of centre of mass does not apply here

Explanation:

Step1: Analyze the symmetry of the original disk

The original disk (1) is symmetric about its center. So, its center of mass is at the center.

Step2: Analyze the new configuration (2)

When the disk is cut into two - halves and arranged as in (2), we can consider the center of mass of each half - disk. Each half - disk has its own center of mass. For a half - disk (semicircular disk), the center of mass is at a distance \(y=\frac{4r}{3\pi}\) from the diameter (where \(r\) is the radius of the original disk). When we stack the two half - disks as in (2), due to the symmetry of the new arrangement about the horizontal line (the line passing through the original center of the disk), the \(x\) - coordinate of the center of mass of the new system (2) is the same as that of the original disk (1). Also, since the mass distribution is symmetric about the horizontal line (the line passing through the original center of mass of the full disk), the \(y\) - coordinate of the center of mass of the new system (2) is the same as that of the original disk (1).

Answer:

C. The same place