Question

Consider the following distribution of objects: a 4.00-kg object with its center of gravity at (0, 0) m, a 1.20-kg object at (0, 6.00) m, and a 1.40-kg object at (4.00, 0) m. Where should a fourth object of mass 7.00 kg be placed so that the center of gravity of the four-object arrangement will be at (0, 0)?

Answer 1

Let the position of the 7 kg particle is (x,y).

Therefore for combined center of gravity, we can write

or,

or,

And for y-position, we can write

or,

or,

Hence, the position of the 7 kg particle should be (-0.8, - 1.03) if the center of gravity of the system is at (0,0).