A particle describes a horizontal circle in a conical funnal whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel ?

Options

A. 2 cm
B. 4 cm
C. 2.5cm
D. 0.25 cm

Answer

C

Explanation

The particle describes the horizontal circle of radius r in the conical funcel . The plane of the circle as at a height h from the vertex of the funel .
for equilibrium , `mg = R sin theta `
` and C.P "force " (mv^(2))/(r ) = R cos theta `
` therefore tan theta = (rg ) /( v^(2) )`
But in ` Delta CAO, tan theta =(r )/(h ) `
`therefore ` From `(1) and (2) , (r ) /( h) = (rg ) /(v^(2))`
` therefore h = (v^(2))/( g) =((0.5)(0.5))/(10) = 0.025 m = 2.5 cm`