I'm not sure but I think there will be no change and I don't get what iPhone means in this question

Solution:

Given:
- Four identical particles, each of mass "m", arranged at the corners of a square of side length "L".

To find:
The shift in the center of mass of the system when the masses are doubled, with respect to the diagonally opposite mass.

Solution:

1. Center of Mass (COM) of the System:
The center of mass of a system of particles is the point where the total mass of the system can be considered to be concentrated. It is the average position of all the particles in the system.

2. Initial Center of Mass (COM) of the System:
- In the initial configuration, the four identical particles are arranged at the corners of a square. The center of mass of this system will be at the center of the square.
- The center of the square coincides with the center of mass of the system.
- Therefore, the initial COM of the system is at the center of the square.

3. Doubling the Masses:
- When the masses of the particles are doubled, the new mass of each particle becomes 2m.
- This doubling of mass does not affect the positions of the particles, only their masses change.

4. Shift in the Center of Mass (COM):
- To find the shift in the center of mass, we need to determine the new position of the center of mass after doubling the masses.
- Since the positions of the particles remain the same, the shift in the center of mass will depend only on the change in the masses.
- The shift in the center of mass will be along the line connecting the initial and final centers of mass, passing through the diagonally opposite mass.

5. Calculation of Shift in the Center of Mass:
- Let's consider the initial center of mass as point O, and the diagonally opposite mass as point A.
- The shift in the center of mass (distance OA) can be calculated using the concept of the center of mass equation.
- The center of mass equation states that the total mass of the system multiplied by the coordinates of the center of mass is equal to the sum of the products of individual masses and their respective coordinates.
- Mathematically, it can be written as M * R_COM = ∑(m_i * r_i), where M is the total mass, R_COM is the position vector of the center of mass, m_i is the mass of the ith particle, and r_i is the position vector of the ith particle.

6. Applying the Center of Mass Equation:
- Let's assume the side length of the square is L.
- The initial center of mass is at the center of the square, which is also the origin, so the position vector of the initial center of mass (R_COM_initial) is (0, 0).
- The final center of mass will also lie on the line connecting the initial center of mass and the diagonally opposite mass.
- Let's assume the coordinates of the final center of mass (R_COM_final) are (x, y).

7. Applying the Center of Mass Equation for x-coordinate:
- Considering the x-coordinate, the center of mass equation becomes:
0 = (2m * 0 + 2m * L + 2m * x + 2m * (-L)) / (2m + 2m + 2m + 2m)
0 = (2m * L + 2m * x -