Question

the maximum and minimum resultant of two force are in the ratio 4:3, the forces are in the ratio?????

Answer 1

Let force be F1 and F2
then maximum resultant = F1+F2
minimum resultant =F1-F2
hence
$\frac{f1 + f2}{f1 - f2} = \frac{4}{3} \\ 3f1 + 3f2 = 4f1 - 4f2 \\ f1 = 7f2 \\ \frac{f1}{f2} = \frac{7}{1}$

Answer 2

The maximum and minimum resultant of two forces are in the ratio 4 : 3.

We have to find the ratio of magnitude of forces.

Concept : Force is a vector quantity. so it follows vector rule to find resultant of any of two forces.

resultant of two different vectors A and B is given by,

$R=\sqrt{A^2+B^2+2ABcos\theta}$,

where θ is angle between the vectors A and B.

now if the θ = 0°

$R=\sqrt{A^2+B^2+2ABcos0^{\circ}}$

$=\sqrt{A^2+B^2+2AB}=|A+B|$

here, |A + B| will be the maximum value of the resultant of two vectors

similarly, if θ = 180° ⇒cos180° = -1

$R=\sqrt{A^2+B^2-2AB}=|A-B|$

here, |A - B| will be the minimum value of the resultant of two vectors.

Now come to the question,

a/c to question,

maximum resultant/minimum resultant = 4/3

⇒|A + B|/|A - B| = 4/3

RHS is positive so we can take only positive value of it as we need to find the ratio of absolute value of A and B.

⇒(A + B)/(A - B) = 4/3

⇒3(A + B) = 4(A - B)

⇒3A + 3B = 4A - 4B

⇒7B = A

⇒A/B = 7/1

Therefore the ratio of magnitude of two forces is 7 : 1.