Question

A stone tied to a string of length \(L\) is whirled in a vertical circle with the other end of the string at 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 its velocity as it reaches a position where the string is horizontal is
(a) \(\sqrt{u^{2}-2 g L}\)
(b) \(\sqrt{2 g L}\)
(c) \(\sqrt{u^{2}-g} \mid\)
(d) \(\sqrt{2}\left(u^{2}-g L\right)\)

Answer 1

Correct Option (d) \(\sqrt{2}\left(\mathrm{u}^{2}-\mathrm{gL}\right)\)
Explanation:
$$
\begin{gathered}
\frac{1}{2} m u^{2}-\frac{1}{2} m v^{2}=m g L \\
v=\sqrt{u^{2}-2 g L} \\
|\vec{v}-\vec{u}|=\sqrt{u^{2}+v^{2}}=\sqrt{u^{2}+u^{2}-2 g L}=\sqrt{2\left(u^{2}-g L\right)}
\end{gathered}
$$

Answer 2

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