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

Options

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

Answer

c

Explanation

Let the distance between two parallel forces `F_(1)` and `F_(2)` be `L` if `r_(1)` is distance of the resultant then equating the moments of the forces
`F_(1) xx r_(1) = F_(2) xx r_(2)` or `(r_(1))/(r_(2)) = (F_(2))/(F_(1))`
Also `r_(1) = (F_(2) L)/(F_(1) + F_(2))`
and `r_(2) = (F_(1)L)/(F_(1) + F_(2))`
As `r_(1) = r_(2) + (L)/(4)`
`:. (F_(2)L)/(F_(1) + F_(2)) = (F_(1)L)/(F_(1) + F_(2)) + (L)/(4)`
`(F_(2))/(F_(1) + F_(2)) = (5F_(1) + F_(2))/(4(F_(1) +F_(2))`
or `5 F_(1) + F_(2) = 4 F_(2)`
`5 F_(1) = 3 F_(2)` or `(F_(1))/(F_(2)) = (3)/(5)` .