Question

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

• A. $\sqrt{\frac{2 gC }{ ab }}$
• B. $2 \sqrt{2 gC }$
• C. $\sqrt{\frac{2 g }{ C }}$
• D. $2 \sqrt{ gC }$

Answer 1

Answer: (B)

$m x \omega^{2} \cos \theta=m g \sin \theta$
$x \omega^{2}=g \tan \theta$
$x \omega^{2}=g \cdot \frac{d y}{d x}$
$x \omega^{2}=g \cdot(8 c x)$
$\omega^{2}=8 g c$
$\omega=2 \sqrt{2 g c}$