Question 129: Work, Energy and Power & Circular Motion

Question

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 the value of $$\omega $$2
 is equal to -

Accepted Answer

In $$\Delta $$ORP,
sin $$	heta $$ = $${{r/2} \over r}$$ = $${1 \over 2}$$ = sin 30
o
$$ \Rightarrow $$ $$	heta $$ = 30
o
As the bead is at rest with respect to the circular ring at position P, The net force on bead is zero.
tan $$	heta $$ = $${{m{\omega ^2}r/2} \over {mg}}$$
$$ \Rightarrow $$ tan 30
o
= $${{{\omega ^2}r} \over {2g}}$$
$$ \Rightarrow $$ $${1 \over {\sqrt 3 }}$$ = $${{{\omega ^2}r} \over {2g}}$$
$$ \Rightarrow $$ $${\omega ^2} = {{2g} \over {r\sqrt 3 }}$$

Answer

$${{\sqrt 3 g} \over {2r}}$$

Answer

$${{2g} \over {\left( {r\sqrt 3 } \right)}}$$

Answer

$${{\left( {g\sqrt 3 } \right)} \over r}$$

Answer

$${{2g} \over r}$$

Work, Energy and Power & Circular Motion

Choose the correct answer: