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Q.
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
ManipalManipal 2011Work, Energy and Power
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
i.e., $T+ m g=\frac{m v_{A}^{2}}{r}$
Tension $(T)$ becomes zero at the points of minimum velocity, therefore
$\therefore 0+ m g=\frac{m v_{A}^{2}}{r}$
$\Rightarrow v_{A}=\sqrt{g r}$
