Question

Two forces $F_1$ and $F_2$ acting at a point have a resultant $F$. lf $F_2$ is doubled, $F$ is also doubled. lf $F_2$ is reversed in direction, then also $F$ is doubled. Then $F_1^2:F_2^2:F^2=$

• A. $3:2:2$
• B. $2:3:1$
• C. $2:2:3$
• D. $2:3:2$

Answer 1

The correct option is D $2:3:2$

$F^2=F_1^2+F_2^2+2F_1{F}_{2}cos\theta$
$4F^2=F_1^2+4F_2^2+4F_1{F}_{2}cos\theta$ (Doubling the value of $F_2$)
$4F^2=F_1^2+F_2^2-2F_1{F}_{2}cos\theta$ (Reversing the direction of $F_2$)
Solving the above equations, we get, $F_2^2=F^2$ and $F_1^2=\frac{3}{2}{F}^2$

Then $F_1:F_2:F_3=\sqrt{3}:\sqrt{2}:\sqrt{2}$