A particle describes a horizontal circle in a conical funne whoses 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. 2 cm
C. 4 cm
D. 2.5 cm

Answer

D

Explanation

Equating the vertical forces , we have
`Nsintheta =mg` ....(i)
and `(mv^2)/(R)=Ncostheta`.......(ii)
`therefore tantheta=(Rg)/(v^2)`........(iii)
Also , in `Delta OAB`,
`tantheta=(R)/(h)` .......(iv)
Equating Eqs. (iii) and (iv) , we get
`h=(v^2)/(g)`
`therefore h=((0.5)^2)/(10)`
`=0.025 m `
`therefore h=2.5cm`