A particle of mass m moving along a straight line experiences force F which varies with the distance x travelled as shown in the figure. If the velocity of the particle at `x_(0)sqrt((2F_(0)x_(0))/m)`, then velocity at `4x_(0)` is

Options

A. `2sqrt((2F_(0)x_(0))/m)`
B. `2sqrt((F_(0)x_(0))/m)`
C. `sqrt((F_(0)x_(0))/m)`
D. none of these

Answer

D

Explanation

Increases in KE =work done
`1/2 mv_(2)^(2)-1/2 mx((2F_(0)x_(0))/m)`
`=1/2(2F_(0)+F_(0))3x_(0)`
`rArr v_(2)=sqrt((11F_(0)x_(0))/m)`