Question

Three particles of masses 0.5 kg 1.0 kg and 1.5 kg are placed at the corner of a right angled triangle as shown in figure locate the centre of mass of the system

Answer 1

Centre of mass is a point where the entire mass is believed to be concentrated at.

If m₁, m₂ have the Coordinates (x ₁, y₁) & (x₂, y₂)

Then Centre of mass is at,

$x _{ CM }= \frac{m_1x_1 + m_2x_2}{m_1 + m_2}$

$y_{ CM }= \frac{m_1y_1 + m_2y_2}{m_1 + m_2}$

We can solve for the Centre of mass by using Coordinate Geometry.

Let, Coordinates of 0.5 kg mass is (0,0)

Position of 1kg mass is ( 4,0)

Position of 1.5kg mass is ( 0, 3)

Now, X coordinate of Centre of mass is,

$= \dfrac{0.5(0) + 1(4) + 1.5(0)}{0.5 + 1 + 1.5} \\ \\ = \dfrac{4}{3}$

Now Y coordinate of Centre of mass is,

$= \dfrac{0.5(0) + 1(0) + 1.5(3)}{3} \\ \\ = \dfrac{3}{2}$

Therefore, The Centre of mass of the system is 4/3 cm towards 1 kg mass and 3/2 cm towards 1.5 kg from 0. 5 kg mass.