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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

u22gL

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B

2gL

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C

u2gL

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D

2(u22gL)

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Solution

The correct option is D

2(u22gL)


Now, since the two velocity vectors shown in Fig. 8.296 are mutually perpendicular, the magnitude of change of velocity will be given by
|Δv|=u2+v2

Substituting the value of v2 from Eq. (i),
|Δv|=u2+u22gL=2(u2gL)


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