Question

a particle is moving in horizontal circle at a height h from the vertex in a conical funnel with uniform speed.find its speed?

Answer 1

the speed of the particle moving in the circular motion is √10h

Let the radius of the circle  be r, mass m, velocity v,  and let N be the force experienced by the particle

The vertical component of N should be equal to the weight

=> Nsin∅ = mg...................eq 1

The horizontal component of N should be equal to the centripetal force, i.e.

Ncos∅ = mv²/r...................eq 2

Dividing eq 1 by eq 2 we get,

tan∅ = gr/v²

But in the cone ,

tan∅ = r/h

Hence,

r/h = gr/v²

=> v² = gh

=> v = √gh = √10h                           (taking g = 10)

Hence the speed of the particle is √10h