# Lesson Worksheet: Center of Gravity of Particles Mathematics

In this worksheet, we will practice finding the position of the center of gravity of a set of particles arranged in a two-dimensional plane.

Q1:

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.

• A cm
• B cm
• C cm
• D cm
• E cm

Q2:

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.

• A
• B
• C
• D
• E

Q3:

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?

• A
• B
• C
• D
• E

Q4:

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 .

Q5:

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.

• A
• B
• C
• D
• E

Q6:

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. Position Mass 𝐴 𝐵 𝐶 𝐷 75 kg 29 kg 71 kg 85 kg
• A
• B
• C
• D

Q7:

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. • A
• B
• C
• D

Q8:

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
• B
• C
• D

Q9:

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. • A
• B
• C
• D

Q10:

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 ?

• A,
• B,
• C,
• D,
• E,

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