Question

Two forces $P$ and $Q$ of magnitude $2F$ and $3F$, respectively, are at an angle $\theta$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle is :

• A. $30^{\circ }$
• B. $60^{\circ }$
• C. $90^{\circ }$
• D. $120^{\circ }$

Answer 1

Answer: (D)

$4F^2+9F^2+12F^2\cos \theta =R^2$
$4F^2+36F^2+24F^2\cos \theta =4R^2$
$4F^2+36F^2+24F^2\cos \theta$
$=4(13F^2+12F^2\cos \theta )=52F^2+48F^2\cos \theta$
$\cos \theta =\frac{12F^2}{24F^2}=-\frac{1}{2}$