Question

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 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. $\frac{3}{5}R$
• D. $\frac{4}{5}R$

Answer 1

Answer: (D)

$\frac{4}{5}R$

From conservation of angular momentum $L_i=L_f$ since there is no external torque acting on the system.
$L_i=M{R}^2\omega$
$L_f=M{R}^2\frac{8\omega }{9}+\frac{M}{8}(\frac{3}{5}R{)}^2\frac{8\omega }{9}+\frac{M}{8}{x}^2\frac{8\omega }{9}$ where x is the distance of the 2nd mass from center.
Solving we get $x=\frac{4R}{5}$