A stone tied to a string of length `L` is whirled in a vertical circle with the ofter end of the string at the centre . At a certin instant of time , the stone is at its lowest position , and has a speed is , the magintube of the change in its velocity as it reached a positive when the string is horizontal is

Options

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

Answer

D

Explanation

Let u be the speed of the stone when the string is horizontal .

Change in KE = change in PE
`(1)/(2)"mu"^(2) - (1)/(2)"mu"^(2) = mgL`
or ` (1)/(2)"mu"^(2) = (1)/(m)"mu"^(2) = mgL`
or ` " " u^(2) = u^(2) -2gL`
Mangitude of change in velocity
`|DeltaV| = sqrt(u'^(2) + u^(2))`
` = sqrt(2(u^(2) -gL))`