question_answer

A rigid bob is fastened to the end of a string and is whirled in a vertical circle of radius r. The minimum speed, bob can have at the highest point of the circle, is

A)  \[\sqrt{rg}\]

B)  \[\sqrt{3\,rg}\]

C)  \[\sqrt{5\,rg}\]                

D)  \[\sqrt{6\,rg}\]

Correct Answer: A

Solution :

                Consider the diagram At the height point P of the circle \[T+mg=\frac{m{{v}^{2}}}{r}\] For bob, to just complete the vertical circle, tension should be equal to zero \[\Rightarrow \]               \[\frac{m{{v}^{2}}}{r}=mg\]where, m = mass of the bob. \[\Rightarrow \]               \[v=\sqrt{rg}\] This is minimum velocity of bob at point P to just complete the vertical circle.