Explanation:

When a disc and a square sheet of the same mass are cut from the same metallic sheet and kept side by side with contact at a single point, the combination's center of mass will be inside the disc. This can be explained through the following points:

1. Distribution of Mass:
The mass of both the disc and the square sheet is distributed differently. The disc has its mass distributed uniformly over its surface, while the square sheet's mass is concentrated around its corners.

2. Contact Point:
When the disc and the square sheet are placed side by side, they will be in contact at a single point. This contact point will be between the disc's center and the square sheet's corner.

3. Center of Mass:
The center of mass of the combination will be the point where the total mass of the system can be assumed to be concentrated. Since the mass of the disc is distributed uniformly, its center of mass will be at its geometrical center. On the other hand, the square sheet's center of mass is at its center. When the two are combined, the center of mass will be closer to the disc's center since it has more mass distributed over a larger area.

4. Calculation:
The exact position of the center of mass can be calculated using the formula:

xcm = (m1x1 + m2x2)/(m1 + m2)

Where x1 and x2 are the distances of the centers of mass of the disc and square sheet from the contact point, and m1 and m2 are their respective masses. Since x1 will be zero (the disc's center of mass is at the contact point), the formula reduces to:

xcm = (m2x2)/(m1 + m2)

Since m1 and m2 are equal, this simplifies to:

xcm = x2/2

This shows that the center of mass is closer to the disc's center (x2) than the square sheet's center (2x2).

Conclusion:
Therefore, it can be concluded that when a disc and a square sheet of the same mass are cut from the same metallic sheet and kept side by side with contact at a single point, the combination's center of mass will be inside the disc.