question_answer

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

Correct Answer: D

Solution :

[d] The particle is moving in circular path form the figure, \[mg=R\sin \theta \]                       (i) \[\frac{m{{v}^{2}}}{r}=R\cos \theta \]                          (ii) From equations (i) and (ii) we get \[\tan \theta =\frac{rg}{{{v}^{2}}}\]but \[\tan \theta =\frac{r}{h}\] \[\therefore h=\frac{{{v}^{2}}}{g}=\frac{{{(0.5)}^{2}}}{10}=0.025m=2.5cm\]