Why does my conical pendulum rod equation give tan θ = (ω²x sin θ)/g?

[pardesi]

i was solving thsi problem
and attempted it in this manner
consider a length $$dx$$ of the rod at a distance $$x$$ from the pivot now
let $$\theta$$ be the required angle
$$dx\cos\theta = dm g$$
$$dx\sin\theta = m\omega^{2}x\sin\theta$$
dividing we get $$\tan\theta = \frac {\omega^{2}x\sin\theta}{g}$$ which is obviously false

 

[bel]

Try drawing a free body diagram, with the three forces of gravity, tension and centripetus.

 

[pardesi]

well what's wrong with my approach

 

[pardesi]

the $$dx$$ should be replaced by $$dT(x)$$ the differential tension.but obviously still the problem is unsolved

 

[learningphysics]

pardesi, I think the problem with this approach is that it assumes that the net force acting on any part of the rod acts radially along the rod. This is not necessarily true.