A bead of mass m stays at point P ( a , b ) on a wire bent in shape of a parabola y=4 Cx ^{2} and ro

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3-2.Motion in Plane

hard

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

A$\sqrt{\frac{2 gC }{ ab }}$

B$2 \sqrt{2 g C}$

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

D$2 \sqrt{ gC }$

(JEE MAIN-2020)

Solution

In rotating frame
$mx \omega^{2} \cos \theta= mg \sin \theta$
$x \omega^{2}= g \tan \theta$
$x \omega^{2}= g \cdot \frac{ dy }{ dx }$
$x \omega^{2}= g \cdot(8 cx )$
$\omega^{2}=8 gc$
$\omega=2 \sqrt{2 gc }$

Standard 11

Physics

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medium

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