Two beads connected by massless inextensible string are placed over the fixed ring as shown in figure. Mass of each bead is $m$ , and there is no friction between $B$ and ring. Find minimum value of coefficient of friction between $A$ and ring so that system remains in equilibrium. ( $C \to $center of ring, $AC$ line is vertical)
  • A$\frac{1}{2}$
  • B$\frac{1}{3}$
  • C$\frac{1}{4}$
  • D$\frac{1}{8}$
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