Answer to Question #192802 in Physics for Hari

Question

A set of point masses is arrayed on the 𝑥𝑦-plane. A mass

of 1 kg is placed at the origin. Two similar masses are at the points

(𝑥, 𝑦) = (1 m, 0) and (0, 1 m), respectively, and a fourth mass of 2 kg

is at the point (1 m, 1 m). (See Fig. 2.4.) (a) Where is the center

of mass? (b) Suppose the fourth mass 1 kg rather 2 kg. Without a

detailed calculation, find the location of the center of mass in this case.

Answer 1

1)

$$x=\frac{1+2}{1+1+1+2}=0.6\ m\\ y=\frac{1+2}{1+1+1+2}=0.6\ m$$

2)

$$x=0.5\ m\\y=0.5\ m$$