Question

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

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

Answer 1

The correct option is D ${120}^o$

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

$\theta ={120}^0$