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

Answer

D

Explanation

`v^(2)=u^(2)-2g t`
Change In the velocity from `A` to `B`
`Deltavec(v)=vec(v_(2))-vec(v_(1))=vec(v_(2))+(-vec(v_(1)))`

`Deltav=sqrt(u^(2)+v^(2))=sqrt(u^(2)+u^(2)-2gL)`
`=sqrt(2(u^(2)-gL))`