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

Answer

A

Explanation

From figure we have, h = 1

`therefore" v=sqrt(u^(2)-2gh)=sqrt(u^(2)-2gl)`
`rArr|Deltav|=|v_(f)-v_(i)|`
= subtraction of vectors at `90^(@)`
`=sqrt(v^(2)+u^(2)=2vu.cos90^(@))`
`=sqrt(v^(2)+u^(2))=sqrt((u^(2)-2gl)+u^(2))=sqrt(2(u^(2)-gl))`