Question

Removing a hole from a plate shifts centroid:

• A. Depends on material
• B. Toward hole
• C. Away from hole
• D. No change

Hint:

Think of the centroid as a balance point.
If you remove weight from the right side (by cutting a hole), the balance point (centroid) must shift to the left (away from the hole) to maintain balance.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks about the direction in which the centroid (geometric center) of a flat plate shifts when a hole is cut or removed from it.

Step 2: Key Formula or Approach:
The centroid coordinates of a composite area with a removed portion are given by:
\[ \bar{x} = \frac{A_1 x_1 - A_2 x_2}{A_1 - A_2} \]
where:
$A_1$ is the original area of the plate, and $x_1$ is its centroid.
$A_2$ is the area of the removed hole, and $x_2$ is the centroid of the hole.

Step 3: Detailed Explanation:

• The centroid represents the geometric center of gravity of an area distribution.

• When a hole is cut out from a symmetric plate, area (mass equivalent) is removed from that specific region.

• The removal of area on one side causes the remaining area to be concentrated more heavily on the opposite side of the hole.

• Mathematically, because we subtract the moment of the removed area ($A_2 x_2$), the center of mass/centroid of the remaining composite shape shifts in the direction opposite to the location of the removed hole ($x_2$).

• Therefore, the centroid always shifts directly away from the center of the removed hole.

Step 4: Final Answer:
Removing a hole from a plate shifts the centroid away from the hole.