Question

Where is the center of mass of a semicircular wire of radius R that is centered on the origin, begins and ends on the x-axis, and lies in the x, y plane?

a) ((0, 0))
b) ((0, R/2))
c) ((0, R/pi))
d) ((0, 2R/pi))

Answer 1

The center of mass of a semicircular wire of radius R that is centered on the origin, begins and ends on the x-axis, and lies in the x, y plane is located at (0, R/pi).

Step-by-step explanation:

The center of mass of a semicircular wire can be found by considering that it lies along the x-axis due to the symmetry of the wire. The x-coordinate of the center of mass is given by the formula:

x = 0

The y-coordinate of the center of mass can be determined by finding the average y-coordinate of all the points along the semicircular arc. Considering that the semicircular arc spans from -R to R in the y-axis, the y-coordinate of the center of mass is given by:

y = R/pi

Therefore, the center of mass of the semicircular wire is located at (0, R/pi).