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Q.

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 M8  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 speed of the system is  89ω and one of the masses is at a distance of  35R from  O. At This instant the distance of the other mass from  O is

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a

23R

b

13R

c

35R

d

45R

answer is D.

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Detailed Solution

Conservation of Angular Momentum, Linititial =Lfinal ⇒MR2ω=MR2+M8×925R2+M8x289ω⇒R2=R289+125+x29⇒R2=R2200+99×25+x29⇒R21−209225=x29⇒x=4R5
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