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.
• B.
• C.
• D.

Answer 1

The correct option is (D)

$\frac{1}{2}m{u}^2-\frac{1}{2}m{v}^2=mgL$

$\Rightarrow v=\sqrt{u^2-2gL}$

$|\overline{v}-\overline{u}|=\sqrt{u^2+v^2}=\sqrt{u^2+u^2-2gL}=\sqrt{2(u^2-gL)}$