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

Answer

D

Explanation

For `tau=0`
`F_(1)(L-x)=F_(2)x`

`F_(2)((3L)/4-x)=F_(1)(x+L/4)(L-x)/(x+(L/4))=x/((3L/4)-x)`
`(3L)/4=x+(3x)/4+x/4=2ximplies3L=8x`
So putting the value of `x`
`F_(1)(5L)/8=F_(2)(3L)/8impliesF_(1):F_(2)=3:5`