Question

three equal maases are kept at P(x1, y1)
Q(x2,
y2)
R(X3.
Y3)
In a coordinate system show that, tgere centre of mass coincides with the centroid of the triangle
PQR​

Answer 1

Question

Three equal masses are kept at P(x₁, y₁), Q(x₂, y₂) and R(X₃, Y₃) in a coordinate system show that, tgere centre of mass coincides with the centroid of the triangle PQR.

Answer

Given :

Three equal masses are kept at P(x₁, y₁), Q(x₂, y₂) and R(X₃, Y₃) in a coordinate system

Solution :

Let the masses of the three particles be m₁, m₂ and m₃ respectively, the centre of mass C of the system of the three particles is defined and located by the co-ordinate les (x, y) given by,

$\sf X = \dfrac{m_1x_1 + m_2x_2 + m_3x_3}{m_1 + m_2 + m_3}$

$\sf Y = \dfrac{m_1y_1 + m_2y_2 + m_3y_3}{m_1 + m_2 + m_3}$

For the particles of equal mass m₁ = m₂ = m₃ = m

$\sf x = \dfrac{m(x_1 + x_2 + x_3)}{3m}$

$\sf x = \dfrac{x_1 + x_2 + x_3}{3}$

$\sf y = \dfrac{m(y_1 + y_2 + y_3)}{3m}$

$\sf y = \dfrac{y_1 + y_2 + y_3}{3}$

Thus, for three particle of equal mass, the centre of mass coincides with the centroid of the triangle formed by the particle.