Question

55. (III) A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate?

Answer 1

Answer:

P = 0.27R from the center

Explanation:

Given,

The radius of the uniform circular plate, R = 2R

The radius of the hole, r = R

The center of the smaller circle from the center is, d = 0.8R

The center of mass of a circular disc with a hole in it given by the formula

                               P = dr²/R² - r²

Where P is the distance from the center of mass located in the line joining the two centers opposite to the hole.

Substituting the given values in the above equation,

                               P = 0.8R x R² / 4R² - R²

                                  = 0.27R³/R²

                                  = 0.27R

Hence the center of mass of plate is at a distant  P = 0.27R from the center