A smooth wire of length 2\pi r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed \omega about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then value of \omega ^{2} is equal to:

 

  • Option 1)

    \frac{\sqrt{3}g}{2r}

  • Option 2)

    2g/(r\sqrt{3})

  • Option 3)

    (g\sqrt{3})/r

  • Option 4)

    2g/r

Answers (1)

N \sin \Theta =m\frac{r}{2}\omega ^{2}

N\cos \Theta =mg

\tan \Theta =\frac{r\omega ^{2}}{2g}\cdots \cdots (1)

from geometry \tan \Theta =\frac{r}{2.\frac{\sqrt{3}}{2}r}\cdots \cdots (2)

equating (1) and (2)

\omega ^{2}=\frac{2g}{\sqrt{3}r}


Option 1)

\frac{\sqrt{3}g}{2r}

Option 2)

2g/(r\sqrt{3})

Option 3)

(g\sqrt{3})/r

Option 4)

2g/r

Most Viewed Questions

Preparation Products

Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Test Series JEE Main 2024

Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 7999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2023

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, Faculty Support.

₹ 9999/- ₹ 6999/-
Buy Now
Knockout JEE Main (One Month Subscription)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, Faculty Support.

₹ 7999/- ₹ 4999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions