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

Solution 52P:

We have to find the position of the center of mass of the resultant larger plate formed due to removal of the small circular plate from it.

Step1 of 6

Concept:

Center of mass(CM) of a body is an imaginary point at which whole mass of the body is supposed to be concentrated.We consider that the net force acts on the centre of mass of body, insteads of considering that it acts on each and every point on the body for simpler calculation and this is one of the importance of application of CM.

The location of the center of mass on the x-axis and y-axis is given as

and

Step 2 of 6</p>

Figure below shows uniform circular plate of radius with a circular hole of radius .

Step 3 of 6</p>

We choose the origin of the coordinate axes to be at the center of the circle of radius .

Radius of the entire uniform circular plate

Radius of the smaller circular hole

It is given that the separation between the center of the smaller circle and the center of the larger circle is

From the symmetry of the system, the y coordinate of the center of mass of the entire circle, the center of mass of the larger part, and the center of mass of the smaller part are all at i.e., on the x-axis. Thus, their y coordinate are equal to zero.