Four objects are situated along the y axis as follows: a 1.91-kg object is at 2.95 m, a 3.05-kg object is at 2.49 m, a 2.60-kg object is at the origin, and a 4.05-kg object is at -0.504 m. Where is the center of mass of these objects? x = m
y = m

x = 0m and y = 0.96m

For a system of masses, the center of mass of these masses is the point at which the masses can be thought of as being most concentrated.

For the four objects, the coordinates of the center of mass G(x, y) is given by;

x = (m₁x₁ + m₂x₂ + m₃x₃ + m₄x₄) / M       (i)

y = (m₁y₁ + m₂y₂ + m₃y₃ + m₄y₄) /M        (ii)

Where;

m₁, x₁ and y₁ = mass, x-position and y-position of object 1

m₂, x₂ and y₂ = mass, x-position and y-position of object 2

m₃, x₃ and y₃ = mass, x-position and y-position of object 3

m₄, x₄ and y₄ = mass, x-position and y-position of object 4

M = the total mass of the objects

From the question;

m₁ = 1.91kg

x₁ = 0   (since it is located at the y axis)

y₁ = 2.95m

m₂ = 3.05kg

x₂ = 0   (since it is located at the y axis)

y₂ = 2.49m

m₃ = 2.60kg

x₃ = 0   (since it is located at the y axis)

y₃ = 0

m₄ = 4.05kg

x₄ = 0   (since it is located at the y axis)

y₄ = -0.504m

M = m₁ + m₂ + m₃ + m₄ = 1.91 + 3.05 + 2.60 + 4.05

M = 11.61kg

Substitute these values into equations (i) and (ii) as follows;

x = ((1.91 x 0) + (3.05 x 0) + (2.60x0) + (4.05x0)) / 11.61

x = 0 / 11.61

x = 0

y = ((1.91 x 2.95) + (3.05 x 2.49) + (2.60x0) + (4.05x-0.504)) / 11.61

y = (5.6345 + 7.5945 + 0 - 2.0412) / 11.61

y = (11.1878) / 11.61

y = 0.96m

Therefore the center of mass of these objects is at x = 0m and y = 0.96m

true

explanation: