Q. 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 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) $\sqrt{u^{2} - g\ L}$
D) $\sqrt{2(u^{2} - g\ L})$
Explanation
(d) The velocity at $B$ is $v$, where
$v^{2} = u^{2} - 2g\ L,$ in vertically upward direction. As is clear from figure change in velocity
[image:4_image115.emf]
${\overrightarrow{\mathbf{OB}}}^{\mathbf{''}}\mathbf{=}\overrightarrow{\mathbf{OA}}\mathbf{=}\overrightarrow{\mathbf{A}^{\mathbf{''}}\mathbf{B}^{\mathbf{''}}}$
$= \sqrt{u^{2} + v^{2}} = \sqrt{u^{2} + \left( u^{2} - 2gL \right)} = \sqrt{2(u^{2} - gL)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.