Question

A stone tied to a string of length $L$ is swired in a verticle circle with the other end of the string at the centre. At a certain instant of time the stone is at it lowest position and has a speed $u$. Find the magnitude of the change in its velocity as it reaches a position, where the string is horizontal.

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

Answer 1

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

By using conservation of energy,

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

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

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

Magnitude of change in velocity = $\sqrt{u^2-2gL+u^2}=\sqrt{2(u^2-gL)}$