A bead of mass m stays at point P(a,b) on a wire bent in the shape of a parabola y=4Cx^2and rotating with angular speed w (see figure). The value of w is neglect friction):
Option: 1 2\sqrt{2gC}
Option: 2 2\sqrt{gC}
Option: 3 \sqrt{\frac{2gC}{ab}}
Option: 4 \sqrt{\frac{2g}{C}}

Answers (1)

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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