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m3 circular motion again - i hate this topic watch

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    a small smooth ring of mass m is threaded on light inelastic string of length 9l whose ends are fixd at a point O on a smooth horizontal table and point A which is at height 6l veritcly above O. The ring moves in horizontal circle on table with string taut. given that the ring is moving at an angular speed of 1/2(g/l)^1/2 calculate the magnitude of the reaction between the ring and the table


    answer is7mg/12
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    resolving forces horizontally:

    T + T cosA = mw²r

    where cosA = 5/13 and r= 2.5l

    => T = mg (5/8)/(18/13) = 65/144 mg


    resolving vertically:

    T sinA + R = mg; sinA = 12/13

    => R = mg(1 - 12/13*65/144) = 7mg/12
 
 
 

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