Worksheet: Finding the Center of Gravity of a Set of Discrete Particles in a Plane

The figure shows three weights arranged in an equilateral triangle of side length 12 cm. Find the coordinates of the center of gravity of the system.

The figure shows a system of point masses placed at the vertices of a triangle. The mass placed at each point is detailed in the table. Determine the coordinates of the center of gravity of the system.

Position
Mass	13 kg	6 kg	15 kg

The figure shows a system of point masses. The mass placed at each point is detailed in the table. Determine the coordinates of the center of mass of the system.

Position
Mass	9 kg	5 kg	4 kg	3 kg

The figure shows three weights arranged in an equilateral triangle of side length 10 cm. Find the coordinates of the center of gravity of the system.

An equilateral triangle of side length 4 cm. The points , , and are the midpoints of , , and , respectively. Weights of 5 kg, 3 kg, 10 kg, 7 kg, 2 kg, and 3 kg are placed at the points , , , , , and , respectively. Find the coordinates of the center of mass of the system.

A square of side length . Three masses of 610 g are placed at , , and . Find the coordinates of the centre of mass of the system.

The figure shows a system of point masses placed at the vertices of a hexagon of side length . The mass placed at each point is detailed in the table. Determine the coordinates of the center of mass of the system.

Position	at	at	at	at
Mass	18 g	26 g	6 g	30 g

A rectangle, , in which and . Four masses of 6, 7, 5, and 9 g placed at the vertices , , , and respectively. Another mass of magnitude 8 grams is attached to the midpoint of . Determine the coordinates of the center of mass of the system.

Four masses of 630 g are placed at the vertices of a square of side length . Determine the coordinates of the center of gravity of the system relative to the axes and .

A square has a sidelength of 70 cm. When four equal masses are placed at the vertices of the square, the center of mass of the system is . When the mass at vertex is removed, the center of mass of the system is . Find the coordinates of the center of mass of the two systems and .

The figure shows a system of point masses . The mass of each point is detailed in the table. Find the coordinates of the center of gravity of the system.

Position	at	at	at	at
Mass	kg	kg	kg	kg

A rhombus in which is located in the first quadrant of a Cartesian plane such that is at the origin and point is on the -axis. Masses of 4 g, 3 g, 6 g, and 10 g are attached at vertices , , and respectively. Find the coordinates of the center of gravity of the system.

The equilateral triangle in the figure has a side length is 36 cm. Point is the intersection of its medians (its centroid) and is the midpoint of . Masses of magnitudes 15 g, 27 g, 40 g, 12 g, and 50 g are fixed at the points , , , , and respectively. Determine the coordinates of the centre of gravity of the system.

A square of side length 3 cm. Four masses of 2, 6, 3, and 2 grams are placed at , , , and respectively. Another mass of 8 g is placed at the midpoint of . Determine the coordinates of the center of mass of the system.

Equal masses are suspended from six of the vertices of a regular octagon . The masses are placed at , , , , , and . Given that the distance from any vertex to the center of the octagon is 52 cm, find the distance between and the center of gravity of the system of the six masses.