The line of action of the resultant of two like parallel forces shifts by one-third of the distance between the forces when the two forces are interchanged. The ratio of the two forces is

Options

A. `1 : 2`
B. `2 : 3`
C. `3 : 4`
D. `3 : 5`

Explanation

`x_(1)=((F_(2)L)/(F_(1)+F_(2)))`
`x_(2)=((F_(1)L)/(F_(1)+F_(2)))`
`x_(1)-x_(2)=(L)/(3)`
`(F_(2)-F_(1))/(F_(1)+F_(2))=(1)/(3)implies 3F_(2)-3F_(1)=F_(1)+F_(2)`
`2F_(2)=4F_(1)`
`(F_(1))/(f_(2))=(1)/(2)`