Three particles of masses 0.50 kg, 1.0 kg and 1.5 kg are placed at the three corners of a right-angles triangle of sides 3.0 cm, 4.0 cm and 5.0 cm as shown in figure. Locate the centre of mass of the system taking O as origin
(1.3 cm, 1.5 cm)
Let us take the 4.0 cm line as the x-axis and the 3.0 cm line as the Y-axis. The coordinates of the three particles are as follows:
mxy0.50 kg001.0 kg4.0 cm01.5 kg03.0
The x - coordinate of the centre of mass is
x = m1x1 + m2x2 + m3x3m1 + m2 + m3
= (0.50 kg).0 + (1.0 kg).(4.0 cm) + (1.5 kg).00.50 kg + 1.0 kg + 1.5 kg
= 4 kg.cm3 kg = 1.3 cm
The y-coordinate of the centre of mass is
y = m1y1 + m2 + m3y3m1 + m2 + m3
= (0.50 kg).0 + (1.0 kg).0 + (1.5 kg)(3.0 cm)0.50 kg + 1.0 kg + 1.5 kg
= 4.5 kg.cm3 kg = 1.5 cm
Thus, the centre of mass is 1.3 cm right and 1.5 cm above the 0.5 kg particle.