Two beads connected by massless inextensible string are placed over fixed ring as shown in figure. M

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4-2.Friction

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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

$\frac{1}{8}$

Solution

$\frac{\mathrm{I}}{\sqrt{2}}=\mathrm{mg}$

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

$\mathrm{mg}=\mu(2 \mathrm{mg})$

$\mu=\frac{1}{2}$

Standard 11

Physics

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