question_answer

A particle describes a horizontal circle on the smooth surface of an inverted cone. If the height of the plane of the circle above the vertex is 9.8 cm, then the speed of the particle will be (Take\[g=9.8\text{ }m/{{s}^{2}}\])

A)  \[0.98\text{ }m{{s}^{-1}}\]    

B)  \[19.6\text{ }m{{s}^{-1}}\]

C)  \[4.9\,m{{s}^{-1}}\]     

D)  None of these

Correct Answer: A

Solution :

 The given situation can be shown as \[R\cos \alpha =\frac{m{{v}^{2}}}{r}\] \[R\sin \alpha =mg\] \[\therefore \] \[\tan \alpha =\frac{gr}{{{v}^{2}}}\] Also         \[\tan \alpha =\frac{r}{h}\] \[\therefore \] \[\frac{r}{h}=\frac{gr}{{{v}^{2}}}\] \[\Rightarrow \] \[{{v}^{2}}=gh=0.98\,m{{s}^{-1}}\]