A thin rectangular plate of uniform area density σ1 = 1.00 kg/m2 has a length a = 0.500 m and a width b = 0.210 m. The lower left corner is placed at the origin, (x, y) = (0, 0). A circular hole of radius r = 0.040 m with center at (x, y) = (0.057 m, 0.057 m) is cut in the plate. The hole is plugged with a disk of the same radius that is composed of another material of uniform area density σ2 = 5.31 kg/m2. What is the distance from the origin of the resulting plate's center of mass?

Answer 1

Original center at (.25 , .105) by symmetry
Original mass = .5*.21*1

added mass = (s2-s1)pi r^2 = 4.31 pi(.04)^2

total mass = original + added

total mass* Xcg = original mass*.25 + added mass*(.057)
solve for Xcg

repeat for Ycg
then Rcg^2 = Xcg^2 + Ycg^2

Answer 2

in a rectangular coordinate system a charge of 25 is placed at the origin of coordinates, and a charge of 25 C is placed at the point x 6m ,Y,0 ..what are the magnitude and direction of the electric field at a,,, X .3m .y.0