Question

Four square table-tops of the same dimensions are shown below. Only the designs of their supports are different from each other. If a person stands upright on the red mark on each of the table, which of the tables will topple? 

• A. A
• B. B
• C. C
• D. D

Hint:

To check for stability, always identify the base of support on the ground. Then, imagine a vertical line coming down from the center of gravity of the object (including any loads). If that line falls inside the base, it's stable. If it falls outside, it will topple. A wider base means more stability.

Answer 1

The Correct Option is B, C, D

Step 1: Understanding the Concept: 
The stability of an object depends on the relationship between its center of gravity (CG) and its base of support. The base of support is the polygon formed by connecting the points where the object touches the ground. An object is stable as long as its combined center of gravity (including any load on it) is vertically above this base of support. If the CG moves outside the base, the object will topple. 

Step 2: Detailed Explanation: 
A person standing on the red mark adds a significant weight, shifting the combined center of gravity of the table-person system towards the red mark. We need to analyze if this new CG is outside the base of support for each table. 
(A) The table has four legs at the corners. The base of support is the large square area between these four legs. The red mark is well inside this area. Even when the person stands on it, the combined CG will almost certainly remain within this large, stable base. Table A will not topple. 
(B) This table has a central stand with two feet. The base of support is the narrow rectangular area connecting the ends of these two feet. The red mark is located far to the side, clearly outside this narrow base. The person's weight will create a large turning moment (torque), and the combined CG will move outside the base of support. Table B will topple. 
(C) Similar to B, this table has a central stand with two feet, although they are spaced wider apart than in B. This creates a wider base of support. However, the red mark is still far from the center and near the edge of the tabletop. The person's weight will shift the CG drastically to the side. It is very likely that the CG will move outside the base of support, causing the table to topple. Table C will topple. 
(D) This table has a cross-legged (scissor) support. The base of support is the rectangle formed by the four points where the legs touch the floor. This base is narrower than the tabletop. The red mark is far outside this support base. The person's weight will pull the combined CG outside this base. Table D will topple. 

Step 3: Final Answer: 
Tables B, C, and D have bases of support that are too small or narrow to support the shifted center of gravity when a person stands on the red mark. Therefore, B, C, and D will topple.