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a smooth hollo cone whose vertical angle is 2 alpha with its axis vertical and vertex downwards revolves about its axis n times per sec. find where a particle may be placed on the inner surface of cone so that it rotates with same speed

a smooth hollo cone whose vertical angle is 2 alpha with its axis vertical and vertex downwards revolves about its axis n times per sec. find where a particle may be placed on the inner surface of cone so that it rotates with same speed

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1 Answers

vikas askiitian expert
509 Points
10 years ago

if the particle is in equilibrium then it will rotate with same apeed as of cone

    for verticle equilibrium

       nsin@=mg

    for horizontal equilibrium

      ncos@=m.w^2.r 

   let the distance between the vertex and the partice along the curved suface be d

     then r=dsin@   

   putting all these values we get

   d=gcot@cosec@/w^2

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