Two forces of magnitudes `3N` and `4N` are acted on a body. The ratio of magnitude of minimum and maximum resultant force on the body is

Explanation

(i)
`theta = 0^(@)`, both the forcees are parallel, R= A+B
`therefore` Net force or resultant force R = 3+4= 7N
`" "` Diretion of resultant is along both the forces

`theta= 180^(@)`, both the forces are antiparallel, R = A`~`B
`therefore ` Net force or resultant force R= 4-3 = 1N
Direction of net force is along larger force i.e. along 4N.
(iii) `theta= 90^(@)`, both the forces are perpendicular

then `R= sqrt (A^(2) + B^(2) + 2AB cos 90^(@))=sqrt (A^(2) + B^(2)) = sqrt(3^(2) + 4^(2))= 5N, tan alpha = (3)/(4) rArr alpha = tan^(-1) ((3)/(4))= 37^(@)`
Magnitude of resultant is 5N which is acting at an angle of `37^(@)` from 4N force.