Question

Calculate the center of mass of three particles kept on the vertices of an equilateral triangle. The masses of the particles are 100 g, 150 g and 200 g. The length of each side of the triangle is 0.5 m.

Answer 1

Given; m₁ = 100 g; m₂ = 150 g; m₃ = 200 g,
l = 0.5 m, x_cm =?, y_cm = ?
From Pythagoras theorem,
AD² = OA² – OD²
= (0.5)² – (0.25)² = 0.25 - 0.0625
or AD² = 0.1875
∴ AD = \(\sqrt{0.185}\) = 0.433m
or AD = 0.433 m
Therefore, the co-ordinates of point O, x₁ = 0, y₁ = 0, coordinates of point B are x₂ = 0.5 m, y₂ = 0
and co-ordinates of points C are x₃ = 0.25 m, y₃ = 0.433 m.
If x_cm and y_cm be the co-ordinates of center of mass then,