Question

A ring of mass M and radius R is rotating with angular speed ω about a fixed vertical axis
passing through its centre O with two point masses each of mass
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 of speed of the system is ω and one of the masses is
at a distance of R from O. At this instant the distance of the other mass from O is

(A) 2/3R           (B) 1 / 3R
(C) 7/ 5R                  (D) 4 / 5R

Answer 1

Let the other mass be at a distance x from the centre. Conserving angular momentum about the axis :

MR2ω=[MR2+M8(35R)2 +M8x2]89ωMR2ω=[MR2+M8(35R)2 +M8x2]89ω

on solving x=45R.
HOPE IT WILL HELP YOU.