Q5.40 A thin circular loop of radius R rotates about its vertical diameter with an angular frequency . Show that a small bead on the wire loop remains at its lowermost point
. What is the angle made by the radius vector joining the centre to the bead in a vertically downward direction
? Neglect friction.
The FBD of the loop is given below :
Using equilibrium conditions we can write :
and
Consider OPQ, we have :
or
Using l in the above equation we get :
or
And
Thus
Since
Substituting the value of in the above equation:-
Thus
or