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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(u2gL)
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Solution

The correct option is D 2(u2gL)

Using conservation of mechanical energy between points A and B

12mu2=12mv2+mgL

v=u22gL

Initial velocity vector=u^i

Find velocity vector=u32gL^j

Change in velocity vector

=u22gL^ju^i

Magnitude of change in velocity vector

=(u22gL)+u2

=2(u2gL)

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