Physics

Physics

Problem

A stone tied to a string of length LL is whirled in a vertical circle with the other end of the string at the centre. At a certain instant, the stone is at its lowest position and has speed uu. What is the magnitude of the change in its velocity as it reaches a position where the string is horizontal? a. u2−2gL\sqrt{u^2 - 2gL} b. 2gL\sqrt{2gL} c. u2−gL\sqrt{u^2 - gL} d. 2(u2−gL)\sqrt{2(u^2 - gL)}
Intuitive explanation

The key is recognizing that velocity is a vector—its magnitude and direction both matter. As the stone moves from the lowest to the horizontal position, you'll use energy conservation to find its new speed, then treat the old and new velocity vectors as arrows and find the magnitude of their difference. The geometry of subtracting two perpendicular vectors of different lengths is what makes this problem interesting.

Intuitive explanation

The key is recognizing that velocity is a vector—its magnitude and direction both matter. As the stone moves from the lowest to the horizontal position, you'll use energy conservation to find its new speed, then treat the old and new velocity vectors as arrows and find the magnitude of their difference. The geometry of subtracting two perpendicular vectors of different lengths is what makes this problem interesting.

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