Centre Of Mass Of Semicircular Ring MCQ - Practice Questions with Answers

Have a look at the figure of semicircular ring.

Since it is symmetrical about y-axis on both sides of the origin

So we can say that  its

And its as  z-coordinate is zero for all particles of semicircular ring.

Now, we will calculate its which is given by

So , Take a small elemental arc of mass dm at an angle   from the x-direction.

Its angular width d 

If the radius of the ring is R then its y coordinate will be Rsin

So,  

As,  

So,