A ring of mass M and radius R is rotating with angular speed abou… - Vidyadip

MCQ

A ring of mass $M$ and radius $R$ is rotating with angular speed $\omega$ about a fixed vertical axis passing through its centre $O$ with two point masses each of mass $\frac{ M }{8}$ at rest at $O$. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is $\frac{8}{9} \omega$ and one of the masses is at a distance of $\frac{3}{5} R$ from $O$. At this instant the distance of the other mass from $O$ is

A
$\frac{2}{3} R$
B
$\frac{1}{3} R$
C
$\frac{3}{5} R$
✓
$\frac{4}{5} R$

✓

Answer

Correct option: D.

$\frac{4}{5} R$

d
Using conservation of angular momentum

$mR ^2 \omega=\left(m R^2 \times \frac{8 \omega}{9}\right)+\left(\frac{ m }{8} \times \frac{9 R^2}{25} \times \frac{8 \omega}{9}\right)+\left(\frac{ m }{8} \times x^2 \times \frac{8 \omega}{9}\right) \Rightarrow x=\frac{4 R}{5}$

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