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

Answer

D

Explanation

Magnitude of change in velocity =`|vecV_p-vecV_A|`
`=sqrt(V_p^2+V_A^2)` ( `because` angle between `vecV_p` and `vecV_A` is `90^@`)
`=sqrt(u^2-2gl+u^2)=sqrt(2(u^2-gl))`