Centre Of Mass Of Semicircular Disc - Practice Questions & MCQ

Have a look at the figure of semicircular disc

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 ring of mass dm of radius x on the disc.

As we know for semicircular ring    

So, for elemental ring  y -coordinate is    

So,     

Have a look at the figure of  semicircular annular ring

It has inner radius as and outer radius as and centre as O

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 an elemental ring of radius r  and it has mass dm and thickness as dr=dx

So y- coordinate of COM of an elemental ring is equal to  

So,  

As  

So