Three particles of masses 0.5 kg, 1.0 kg and 1.5 kg are placed at the three corners of a right angled 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.

Explanation

taking x and y axes as shown.
coordinates of body A = (0,0)
coordinates of body B = (4,0)
coordinates of body C = (0,3)
x - coordinate of c.m. `=(m_(A)x_(A)+m_(B)x_(B)+M_(C)r_(C))/(m_(A)+m_(B)+m_(C))`
`=(0.5xx0+1.0xx4+1.5xx0)/(0.5+1.0+1.5)`
`=(4)/(3) (cm)/(kg)=cm=1.33cm`
similarly y - wordinates of c.m.
`=(0.5 xx0+1.0xx0+1.5xx3)/(0.5+1.0+1.5)=(4.5)/(3)=1.5 cm`
So, certre of mass is 1.33 cm right and 1.5 cm above particle A.