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)
Difficult
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$\frac{\mathrm{I}}{\sqrt{2}}=\mathrm{mg}$
$\frac{\mathrm{I}}{\sqrt{2}}=\mu \mathrm{N}=\mu\left(\mathrm{mg}+\frac{\mathrm{I}}{\sqrt{2}}\right)$
$\mathrm{mg}=\mu(2 \mathrm{mg})$
$\mu=\frac{1}{2}$
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