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 $u$. Determine the magnitude of the change in its velocity as it reaches a position where the string is horizontal is:

• A. $\sqrt{u^2-2gL}$
• B. $\sqrt{2gL}$
• C. $\sqrt{u^2-gL}$
• D. $\sqrt{2(u^2-2gL)}$

Answer 1

The correct option is A $\sqrt{u^2-2gL}$

From energy conservation:

$E_A=E_B$

$⟹\frac{1}{2}m{u}^2=\frac{1}{2}m{V}^2+mgl$

$⟹\frac{1}{2}{u}^2=\frac{1}{2}{V}^2+gl$

$⟹V^2=u^2-2gl$

$⟹V=\sqrt{u^2-2gl}$