A particle describes a horizontal circle of radius 'r' in conical funnel with smooth inner surface with a speed of 0.5 m/s. The height of the plane of the circle from the vertex of the funnel is (acceleration due to gravity, g = 10 , m/s ^2 )

Step-by-step solution

Let be the semi-vertical angle of the conical funnel. The radius of the circular path is r and its height from the vertex is h . From the geometry of the cone, we have: = r h The forces acting on the particle are its weight mg acting vertically downwards and the normal reaction N acting perpendicular to the inner surface of the funnel. The normal reaction makes an angle with the horizontal. Resolving N into vertical and horizontal components, we get: N = mg N = mv^2 r Dividing the vertical component by the horizont