A particle fall freely from height s . At certain height its kinetic energy is three time to its potential energy ,them at any one instant its height and speed respectively `…………..`

Options

A. `s/4,(3gs)/2`
B. `s/4,(sqrt(3gs))/2`
C. `s/2,(sqrt(3gs))/2`
D. `s/4,sqrt((3gs)/2)`

Answer

B

Explanation

Suppose AC = s and particle fall from point A and v its velocity at point B .
` :. V^(2)-v_(0)^(2) =2g (s-x)`
`v^(2)=2g(s-x)`
Potential energy at B = mgx `…….` (2)
` :. ` Kinetic energy at pont B .
= 3x potential energy .
`1/2 m ss 2g(s-x) = 3 mgx `
` :. s - x = 3x `
` :. s = 4x `
` :. x = S/4`
` :. ` equation (1) ,
`v^(2) =2g(s-s/4)`
`= 2g xx (3s)/4 `
`=(3gs)/2 `
` :. v = sqrt((3gs)/2)`.