A stone is tied to a string of length $l$ and is whirled in a vertical circle with the other end of

Question

A stone is tied to a string of length $l$ and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in velocity as it reaches a position where the string is horizontal ( $g$ being acceleration due to gravity) is\

Professor PC Thomas Classes · Answer

(a) : The total energy at $A=$ the total energy at $B$\ $\Rightarrow \frac{1}{2} m u^{2}=\frac{1}{2} m v^{2}+m g l$\ $\Rightarrow \quad v=\sqrt{u^{2}-2 g l}$ $$ d_{A} $$ The change in magnitude of velocity $=\sqrt{u^{2}+v^{2}}$ $$ =\sqrt{2\left(u^{2}-g light)} $$