A circular plate of uniform thickness has a diameter of 56cm.A circular portion of diameter 42cm is removed from one edge of the plate .find the position of the center of mass of the remaining portion.

Answer 1

The removed portion has 3/4 the diameter and 9/16 of the area and mass M of the full circular (56 cm dia) plate.

Measure CM location from the center of the larger full circle. The center of the cutout circular hole is 7 cm from the center of the large circle

[M - (9/16)M]*x = M*0 - (9/16)M*7
(7/16)x = -63/16
x = 63/7 = -9.0 cm

The CM is 9 cm from the center of the large circle, in the opposite direction from the center of the removed circle