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

R.E.F image

From Energy conservation

$V^2=U^2-2gL$ ___(1)

$\left|△\overline{V}\right|=\sqrt{V^2+U^2}$

from eq(i)

$\left|△\overline{V}\right|=\sqrt{U^2+U^2-2gL}$

$\left|△\overline{V}\right|=\sqrt{2(U^2-gL)}$