# A bead of mass m stays at point P(a,b) on a wire bent in the shape of a parabola and rotating with angular speed (see figure). The value of is neglect friction): Option: 1 Option: 2 Option: 3 Option: 4

First Draw FBD for point P

$For \ y=4Cx^2 \\ \Rightarrow \frac{dy}{dx}=8Cx=tan\theta$

$\begin{array}{l} \text{Along tangential direction of P} \\ m x \omega^{2} \cos \theta=m g \sin \theta \\ x \omega^{2}=g \tan \theta \\ x \omega^{2}=g \cdot \frac{d y}{d x} \\ x \omega^{2}=g \cdot(8 Cx) \\ \omega^{2}=8 g C \\ \omega=2 \sqrt{2 g C} \end{array}$

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