Question

Consider the following distribution of objects: a 4.00-kg object with its center of gravity at (0,0) m, a 5.20-kg object at (0,5.00) m, and a 5.40-kg object at (4.00,0) m. Where should a fourth object of mass 9.00 kg be placed so that the center of gravity of the four-object arrangement will be at (0,0) ?

Answer 1

let the coordinates of the forth object is (x , y)

for the center of gravity at (0 , 0)

0 = (4 * 0 + 5.2* 0 + 5.4 * 4 + 9 * x)/(4 + 5.2 + 5.4 + 9)

solving for x

x = -2.4 m

Now , for the y coordinate

0 = (4 * 0 + 5.2* 5 + 5.4 * 0 + 9 * y)/(4 + 5.2 + 5.4 + 9)

y = -2.89 m

the center of gravity is (-2.4 , -2.89 ) m