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 lowest position and has a speed `u` . Find the magnitude of the change in its velocity as it reaches a position, where the string is horizontal.

Options

A. `sqrt(u^(2)-2gL)`
B. `sqrt(2gL)`
C. `sqrt(u^(2)-gL)`
D. `sqrt(2(u^(2)-gL))`

Answer

D

Explanation

From energy conservation
`v^(2)=u^(2)-2gL.....(1)`
Now, since the two velocity vectors shown in figure are mutually perpendicular, hence the magnitude of change of velocity will be given by
`|Deltavec(v)|=sqrt(u^(2)+v^(2))`
Substituting value of `v^(2)` from
Equation (1)
`|Deltavec(v)|=sqrt(u^(2)+u^(2)-2gL)`
`|Deltavec(v)|=sqrt(2(u^(2)-gL))`