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WHY IS CENTRE OF MASS OF 2 PARTICLES IS IN BETWEEN THE LINE JOINING 2 OBJECTS?  
Asked by kavukattunora | 25 Nov, 2020, 09:56: AM
answered-by-expert Expert Answer
Let (x1 , y1 , z1 ) be the center of mass of object-1 and (x2 , y2 , z2 ) be the centre of mass of object-2. 
Let these coordinates are assigned with respect to some coordinate sytem and originf
 
centere of mass of combined system of object-1 and object 2 with respect to the origin of the considered coordinate system is given as
 
X = ( m1 x1 + m2 x2 ) / ( m1 + m2 )
 
Y = ( m1 y1 + m2 y2 ) / ( m1 + m2 )
 
Z = ( m1 z1 + m2 z2 ) / ( m1 + m2 )
 
Now let us choose the coordinate system so that one of the axis, say x-axis,  lying on the line connecting centre of masses of object-1 and object-2 .
 
Then transformed coordinates of centre of mass of combined system are given as
 
X' =  ( m1 x1'   + m2 x2' ) / ( m1 + m2 ) 
 
Y' = 0
 
Z' = 0 
y and z coordinates of transformed coordinate system is zero , because both of center of masses of object-1 and object-2 are at x-axis.
 
Hence it is proved that center of mass of combined system two objects lie in the line connecting the centre of mass of individual objects.
Answered by Thiyagarajan K | 25 Nov, 2020, 15:31: PM

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