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( 2(u^(3)-gL))`
B. `=sqrt( 2(u^(2)-L))`
C. `=sqrt( 3(u^(2)-gL))`
D. `=sqrt( 2(u^(2)-gL))`

Answer

D

Explanation

`v=sqrt(u^(2)-2gh)=sqrt(u^(2)-2gL)`
`|DeltaV|=|v_(f)-v_(i)|`
`=sqrt(v^(2)+u^(2)-2v.ucos90^(@))`
`=sqrt((u^(2)-2gH)+u^(2))`

`=sqrt( 2(u^(2)-gL))`