A uniform wire is bent into a semi-circle of radius R and laid out such that it is entirely in the x-y plane .The semicircle has its ends fixed on the x axis at x = -R and x = +R.With the exception of its end points,the semicircle is entirely above the x-axis (i.e.the y-coordinates of all points on its arc are positive).What is the y coordinate of its center-of-mass?
A)2R/$\pi$
B)R/3
C)R/2
D)2R
E)R/ 

Question

Quizplus · Accepted Answer

The center of mass of a uniform semi-circular wire is located at a distance of $ \frac{2R}{\pi} $ from the center of the circle along the perpendicular bisector of the diameter, which in this case is the y-axis. Therefore, the y-coordinate of the center of mass is $ \frac{2R}{\pi} $.

A Uniform Wire Is Bent into a Semi-Circle of Radius π\piπ

A Uniform Wire Is Bent into a Semi-Circle of Radius $\pi$