Question

A smooth hollow cone whose vertical angle is 2alpha with it axis vertical and vertex downwards, revolves about its axis n times per seconds. Find distances from axis of rotation where a particle may be placed on the inner surface of cone so that it rotates with same speed -

Answer 1

Answer:

d=gcot@cosec@/w^2

Explanation:

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

for vertical 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

   

  m = n/g sin@

  ncos@=m.w^2.r  

 ncos@=n/g x sin x w^2.r

  now;

  r= dsin@

  n cos@=n/g x sin x w^2.r

  ncos@=n/g x sin x w^2.dsin@

Simplifying above equation;

  d=gcot@cosec@/w^2

Answer 2

Answer:

your answer is in the photo , this answer is correct.