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?
√2(u2−gL)
Applying energy conservation, we get final velocity, v=√u2−2gL.
In vector form, we can express final velocity →v=√(u2−2gL) ^j and initial velocity →u=u ^i.
Now, the magnitude of the change in its velocity =√u2+v2=√2(u2−gL).