Lesson Worksheet: Center of Gravity of Particles Mathematics

In the given figure, three weights of magnitudes 2 N, 5 N and 3 N are placed on the vertices of an equilateral triangle of side length 8 cm.

Find the center of gravity of the system.

Three particles are placed on a line. Particle of mass 4 kg is located at the origin, particle of mass 6 kg at , and particle of mass 10 kg at . Determine the coordinates of the center of mass of the three particles.

Four particles of masses 9 kg, 10 kg, 4 kg, and 7 kg are placed on the -axis at the points , , , and respectively. What is the position of the center of mass of the four particles?

The points , , and on the -axis are occupied by three solids of masses 9 kg, 6 kg, and kg respectively. Determine the value of given the center of mass of the system is at the point .

Suppose three masses of 1 kg, 4 kg, and 6 kg are located at points whose position vectors are , , and . Determine the position vector of the center of gravity for this system of masses.

The figure shows a system of point masses placed at the vertices of a square of side length 6 units. The mass placed at each point is detailed in the table. Determine the coordinates of the center of gravity of the system.

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

In a rectangle , and . Four masses of 6, 7, 5, and 9 g are 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 given that C is placed at the origin, and the scales of the axes are defined such that each unit represents 1 cm of distance.

A triangle , where , , , and and are the midpoints of and respectively, is located in the first quadrant of a Cartesian plane such that is at the origin, and the point is on -axis. Three equal masses are placed at points , , and . Determine the coordinates of the center of gravity of the system.

Suppose three masses of 6 kg, 9 kg, and kg are at points , , and respectively. If the center of mass of the three masses is , what are the values of and ?