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)-2 gL`
B. `sqrt2g L`
C. `sqrt u^(2)- gL`
D. `sqrt (2(u^(2)-gL))`

Answer

D

Explanation

`v_(L)=u,v_(h)=sqrt(v_(L)^(2)-2gh)=sqrt((u^(2))-2gl`
`v_(L) and v_(h)` are tan to each other then their resultant is ,
`v_(R)=sqrt(v_(L)^(2)+v_(h)^(2))=sqrt(u^(2)+u^(2)-2gl)`
` =sqrt(2u^(2)-2gl)`
`=sqrt(2(u^(2)-gL))`