Question

Two equal forces have their resultant to either. At what angle are they inclined?

• A. $\Rightarrow \theta =0^o$
  
• B. $\Rightarrow \theta ={120}^o$
  
• C. $\Rightarrow \theta ={150}^o$
  
• D. $\Rightarrow \theta ={10}^o$
  

Answer 1

The correct option is B $\Rightarrow \theta ={120}^o$

Here $A=F;B=F;R=F;\theta =?$
Now $R=\sqrt{A^2+B^2+2AB\cos \theta }$
$F=\sqrt{F^2+F^2+2F.F.\cos \theta }$
$=F\sqrt{2(1+\cos \theta )}$
$\Rightarrow 1=2(1+\cos \theta )$
$\cos \theta =-\frac{1}{2}=\cos {120}^o$
$\Rightarrow \theta ={120}^o$