irodov one

Is it tuff ??
As far as I know ...
We need just 2 eqn

Tcosθ=mg ----(1)
Tsinθ=mω²r ----(2)

U should get the answer from here..

I hope I am not making a fool out of myself :P

well i have a pbm in writing the force equation.in this case it is a chain na.So how we shud write the force equation.Can u explain wat u have done.

i wrote the force eqn at that pont where thread is joined to chain

hmm....let Nishant sir or anant sir then handle it ....
Ofcourse irodov questions are weird..[3]

Let the distance of the center-of-mass from the axis be ρ. Write down the equations for the center of mass:

Along the vertical: T cos θ = mg
Along the horizontal: T sin θ = m ω² ρ

Dividing

ω²Ïg = tan θ ==> ρ = g tan θω²

This is precisely what eureka wrote. However, the point is that the equations pertain to the center of mass and not the point where the thread is joined to the chain.

Thanx sir for correcting me [1]

thanq sir.At first i also done the same wat eure but my logic is rong.Dats y i posted here.Thanx for helping.

i beleive what isaid in my st post was OK...
we take mass dm of that part of chain to which thread is attached..and then write the smae eqn..after all we just need to find r and T

@msp, on the center of mass the external forces act exactly along their original directions.

sir can u pls explain why it shud be