A stone is tied to a string of length l and is whirled in a vertical circle with the other end of the string as 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 velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is

Options

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

Answer

B

Explanation

`W_(mg)=DeltaKimplies-mg l=(1)/(2)mv^(2)-(1)/(2)mu^(2)`
or `mv^(2)=m(u^(2)-2gl)` or v=`sqrt(u^(2)-2gl)hatj`
`vecu=uhati`
`therefore vecu-vecu=sqrt(u^(2)-2gl)hatj-uhati`
`therefore|vecv-vecu|=[u^(2)-2gl+u^(2)]^((1)/(2))=sqrt(2(u^(2)-gl))`