A tabletop gamer has designed a game that requires three dice to be thrown onto a tray with a measurement grid. To add an extra degree of randomness, the coordinates of the center of mass of the three dice are used as well. The masses of the three dice are 11.10 g, 15.10 g, and 18.90 g, and their respective coordinates after one particular throw are (0.3150 m,−0.4990 m), (−0.4050 m,0.4850 m), and (−0.1150 m,−0.1850 m). Requried:
What are the resulting coordinates of the center of mass of the dice, xcm and ycm?

The resulting coordinate is  

Explanation:

From the question we are told that  

     The  mass of the first dice is  

      The  mass of the second dice is  

     The mass of the third dice is  

     The coordinate of the first dice is

     The coordinate of the second dice is  

      The coordinate of the third dice is  

Generally the resulting coordinate of the center of mass of the dice in the x-axis is mathematically evaluated as

i.e the summation of the moments about their x-axis divided by the magnitude of their masses

    substituting values

Generally the resulting coordinate of the center of mass of the dice in the y-axis is mathematically evaluated as

Thus the resulting coordinate is  

0.55x745.7j and a calculator