four particles each of mass 1kg at rest of four corners of a square as shown in the fig . find the coordinates of the mass of the system
since the masses are equal, and at equal distances from the center of the square, the center of mass is the center of the square.
To find the coordinates of the center of mass of the system, we need to calculate the coordinates by taking into account the masses and positions of each particle.
Since each particle has a mass of 1kg and is at rest, it means they are stationary and not moving. This simplifies the calculation.
Let's assume the sides of the square have a length of "a" units. The square can be positioned in a coordinate system such that the bottom-left corner of the square is at the origin (0,0).
Since all particles have the same mass of 1kg, the center of mass will be located at the average position of all four particles.
Let's calculate the x-coordinate of the center of mass first. Since the two particles on the right side of the square have the same x-coordinate (a), and the two particles on the left side of the square have the same x-coordinate (-a), the x-coordinate of the center of mass is:
x-coordinate = (2a + (-2a)) / 4 = 0 / 4 = 0
Next, let's calculate the y-coordinate of the center of mass. The two particles on the top side of the square have the same y-coordinate (a), and the two particles on the bottom side of the square have the same y-coordinate (-a), the y-coordinate of the center of mass is:
y-coordinate = (2a + (-2a)) / 4 = 0 / 4 = 0
Therefore, the coordinates of the center of mass of the system are (0, 0).