Question

Two equal forces have their resultant equal to either. find the angle between them

Answer 1

check the attachment

Answer 2

Let us consider two forces F and F'.

As per the question F = F'

The magnitude of resultant of these two forces are equal to either.

Hence. F = F' = R.

Let the angle between F and F' is $\theta$

As per parallelogram law of vector addition,

                                $R=\sqrt{ F^{2} +F'^{2} +2FF'cos\theta}$

                                        $=\sqrt{ R^{2}+ R^{2} +2R.Rcos\theta}$

                                        $=\sqrt{2 R^{2} +2R^{2}cos\theta}$

                                        $=\sqrt{2 R^{2} [1+cos\theta]}$

        Squaring both sides we get-

                                          $R^{2} =2R^{2}[1+cos\theta]$

                                     ⇒     $\frac{1}{2} =1+cos\theta$

                                     ⇒     $cos\theta=\ -\frac{1}{2}$      

                                      ⇒   $\theta=\ 120^{0}$    [ans]