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

Options

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

Answer

D

Explanation

The particle is moving in circular path. From the figure, `mg=Rsintheta` (i)
`(mv^(2))/(r)=Rcostheta` (ii)
From equation (i) and (ii) we get
`tantheta=(rg)/(v^(2)` but `tantheta=(r)/(h)`
:. `h=(v^(2))/(g)=((0.5)^(2))/(10)`
`=0.025m=2.5cm` .