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WHY IS CENTRE OF MASS OF 2 PARTICLES IS IN BETWEEN THE LINE JOINING 2 OBJECTS?

 

Asked by kavukattunora 25th November 2020, 9:56 AM
Answered by 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 Expert 25th November 2020, 3:31 PM
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