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 cgange in its velocity as it reaches a position, where the string is horizontal.

Options

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

Answer

D

Explanation

Applying energy conservation-
`1/2 mu^(2) = mgL + 1/2 mv^(2) rArr v = sqrt(u^(2) - 2gL)`
Change in velocity
`|Deltavecv| = sqrt(u^(2) + v^(2)) = sqrt(u^(2) + u^(2) - 2gL) = sqrt(2(u^(2) - gL))`