Question 132: Work, Energy and Power & Circular Motion

Question

A bead of mass m stays at point P(a, b) on a
wire bent in the shape of a parabola y = 4Cx
2
and rotating with angular speed $\omega $ (see figure).
The value of $\omega $ is (neglect friction) :
![](https://imagex.cdn.examgoal.net/jgy2xukev0n6nt/28d3025a-6c01-4167-b59a-b354236e1833/ac828690-f267-11ea-8293-3b6cc591631c/file-jgy2xukev0n6nu-285w.png)

Accepted Answer

y = 4Cx
2
$ \Rightarrow $ $\frac{dy}{dx}  $ = tan $	heta $ = 8Cx
At P, tan ÃÂ¸ = 8Ca
For steady circular motion
mg sinÃÂ¸ = mÃÂ
2
acosÃÂ¸
$ \Rightarrow $ tan $	heta $ = $\frac{\omega^{2} a}{g} $
$ \Rightarrow $ 8Ca $ 	imes $ g = ÃÂ
2
$ 	imes $a
$ \Rightarrow $ $\omega $ = $\sqrt{8gC} $
$ \Rightarrow $ $\omega $ = $2\sqrt {2gC} $
![](https://imagex.cdn.examgoal.net/1ki3e6y0s/6d521a9d-457f-41e1-9228-06f9aa88064e/94079fc0-3267-11eb-bf8e-9bdae134a25b/file-1ki3e6y0t-860w.jpeg)

Answer

$2\sqrt {2gC} $

Answer

$2\sqrt {gC} $

Answer

$\sqrt {{{2gC} \over {ab}}} $

Answer

$\sqrt {{{2g} \over C}} $

Work, Energy and Power & Circular Motion

A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx 2 and rotating with angular speed \omega (see figure). The value of \omega is (neglect friction) :

Choose the correct answer: