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 ? [J&K CET 2005]            

A)                                  0.25 cm                      

B)                         2 cm            

C)                         4 cm               

D)                         2.5 cm            

Correct Answer: D

Solution :

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