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The bowling pin shown in the figure has uniform density. Based on the symmetry of the bowling pin, along which dashed line must the center of mass be located?

A is  A      B IS B             C IS C        D IS D

In the image, the bowling pin has dashed lines labeled \( A \), \( B \), \( C \), and \( D \). Based on the symmetry of the bowling pin and the fact that it has uniform density, the center of mass must lie along the axis of symmetry.

Looking at the shape, it is symmetric about the vertical dashed line labeled \( C \). This line divides the pin into two identical halves, and since the object has uniform density, the center of mass will be located along this vertical axis.

Thus, the center of mass must be located along line \( C \).

Would you like further details on symmetry or center of mass? Here are five related questions:

1. How does symmetry influence the position of the center of mass?
2. Can an object with uniform density have its center of mass outside the object?
3. What are the mathematical methods to calculate the center of mass for non-uniform objects?
4. How would the center of mass shift if the bowling pin were not symmetric?
5. What other physical properties depend on the center of mass?

**Tip**: When solving for the center of mass of irregular objects, break the object into smaller, simpler shapes and sum the contributions from each.

The bowling pin shown in the figure has uniform density. Based on the symmetry of the bowling pin, along which dashed line must the center of mass be located? A is A, B is B, C is C, D is D.

Learn how the symmetry of a bowling pin affects the location of its center of mass. This problem involves understanding the concept of symmetry and applying the center of mass theorem. Suitable for students in Grades 9-12.

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