Question

The resultant of two forces $3P$ and $2P$ is $R.$ If first force is doubled then the resultant is also doubled. The angle between the forces is

• A. $60°$
• B. $30°$
• C. $120°$
• D. $150°$

Answer 1

The correct option is C $120°$

Resultant of two force
$R^2=(3P{)}^2+(2P{)}^2+12P^2\cos \theta$
$\Rightarrow R^2=P^2(13+12\cos \theta )\cdots \left(1\right)$

If first force is doubled then, the resultant is also doubled
$(2R{)}^2=(6P{)}^2+(2P{)}^2+24P^2\cos \theta$
$\Rightarrow 4R^2=P^2(40+24\cos \theta )\cdots \left(2\right)$

Dividing the equation $1$ and $2$,
$4=\frac{40+24\cos \theta }{13+12\cos \theta }$
$\Rightarrow 52+48\cos \theta =40+24\cos \theta \Rightarrow \cos \theta =-\frac{1}{2}\Rightarrow \theta ={120}^{\circ }$