question_answer

A fighter plane is moving in a vertical circle of radius r. Its minimum velocity at the highest point A of the circle will be

A) \[\sqrt{3gr}\]                    

B)         \[\sqrt{2gr}\]

C)  \[\sqrt{gr}\]                     

D)        \[\sqrt{gr/2}\]

Correct Answer: C

Solution :

When a body tied to the end of a string is revolved in a vertical circle, the speed of the body is different at different points of the circular paths. The resultant of tension\[(T)\]and weight\[(mg)\]provider the necessary centripetal force \[ie,\]    \[T+mg=\frac{mv_{A}^{2}}{r}\] Tension\[(T)\]becomes zero at the points of minimum velocity, therefore \[\therefore \]  \[0+mg=\frac{mv_{A}^{2}}{r}\] \[\Rightarrow \]               \[{{v}_{A}}=\sqrt{gr}\]