Thanks a lot...
my fault was actually i assumed the cone to be hollow but it is solid...!
so h/4 not h/3 is the location of its center of mass from base... got it now..!
Suppose there's a hemisphere of radius R (say) and a right cone of same radius R but ht. R/2 is scooped out of it then i have to find the center of mass of the remaining part.
Here's how i approached...
clearly by symmetry, Xcm = 0
Now, Let M be the mass of the hemisphere so...
On finding the center of mass of a solid hemisphere i came up with some different result.
Here's what i did...
consider a small ring at a distance r from the center of the hemisphere and one more ring at a distance
of r+dr from center of the ring.
let, mass of the small element formed...
can you tell me the position of the center of mass of a ring of radius R and mass M?
Does it lie on the circumference or somewhere else when origin is assumed to be at the
center of the diameter joining the two ends of the ring?
A silly doubt regarding center of mass...
As we know for bodies having continuous distribution of mass we can know their center of mass by the method of integration...
like, Xcm = 1/M∫x.dm
but what is x here?
in many cases...
like in finding the COM of a ring
Xcm = 0 and Ycm = 2r/∏...