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

Answer 1

The correct option is D $\sqrt{2(u^2-gL)}$


Using conservation of mechanical energy between points A and B

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

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

$\text{Initial velocity vector}=u\hat{i}$

$\text{Find velocity vector}=\sqrt{u^3-2gL}\hat{j}$

Change in velocity vector

$=\sqrt{u^2-2gL}\hat{j}-u\hat{i}$

Magnitude of change in velocity vector

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

$=\sqrt{2(u^2-gL)}$