Question

Find the centre of mass of 3 particles of masses 3kg, 2kg and 5kg which are at points (2,-1)(4,5)(6,7)​

Answer 1

Explanation:

According to the definition of centre of mass, we can imagine one particle of mass (1+2+3)kg at (1,2,3); another particle of mass (2+3)kg at (−1,3,−2).

Let the third particle of mass 5kg put at (x3,y3,z3) i.e.

m1=6kg,(x1,y1,z1)=(1,2,3)

m2=5kg,(x2,y2,z2)=(−1,3,−2)

m3=5kg,(x3,y3,z3)=?

Given, (XCM,YCM,ZCM)=(1,2,3)

Using XCM=m1 x 1 + m2 x 2+ m3 x3 m1 + m2 + m3

1=6×1+5×(−1)+5x36+5+5

5x3=16−1

=15 or x3=3

Similarly, y3=1 and z3=8