Question

A particle describes a horizontal circle in a conical funnel 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?

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

Answer 1

The correct option is D 2.5 cm

The particle is moving in circular path
From the figure, mg = Rsin $\theta$ ..(i)
$\frac{m{v}^2}{r}$ = R cos $\theta$ ..(ii)
From equation (i) and (ii) we get
tan $\theta$ = $\frac{rg}{v^2}$ but tan $\theta$ = $\frac{r}{h}$
$\therefore$ h = $\frac{v^2}{g}$ = $\frac{{\left(0.5\right)}^2}{10}$ = 0.025 m = 2.5 cm