Question

You are supplied with three identical rods of same length and mass.If the length of each rod is 2π. Two of them are converted into rings and then placed over the third rod as shown in figure. If point A is considered as origin of the coordinate system the coordinate of the centre of mass will be ( you may assume AB as x axis of the coordinate system)

Answer 1

The two rings have a radius of

$$R=L/(2\pi)=(2\pi)/(2\pi)=1.$$

The x-coordinate of the centre of mass, since the system is symmetrical, is at the midpoint, i.e. at $\pi$ from the end of the rod at the bottom.

Three rings and the rod have their center of mass along y-axis respectively at $y_1=R,\space y_2=R, \space y_3=0.$ So, the y-coordinate is

$$y_c=\frac{y_1m+y_2m+y_3m}{3m}=\frac{\pi m+\pi m+0\cdot m}{3m}=2\pi/3.$$