Calculation of Center of Mass: Practice Problem & Solution
The centre of mass of three particles of masses 1 kg, 2 kg and 3 kg is at (3, 3, 3) with reference to a fixed coordinate system. Where should a fourth particle of mass 4 kg be placed so that the centre of mass of the system of all particles shifts to the point (1, 1, 1)
Solution Explained:
To solve this problem, we apply the core principles of Calculation of Center of Mass. Understanding the underlying formula is key to arriving at the correct answer below:
Center of mass of 1 kg, 2 kg and 3 kg is at (3, 3, 3) so, 6kg can be assumed to present at (3, 3, 3).
Assume 4 kg is placed at (x,y,z) Center of mass is at (1,1,1)
1= (4x+6×3)/10
x=-2
similarly y=-2 and z=-2
COM(-2,-2,-2)
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