Question

One of the two forces is double and the other resultant is equal to the greater force. The angle between then is

• A. $co{s}^{-1}\left(1/2\right)$
• B. $co{s}^{-1}(-1/2)$
• C. $co{s}^{-1}\left(1/4\right)$
• D. $co{s}^{-1}(-1/4)$

Answer 1

The correct option is D $co{s}^{-1}(-1/4)$

Let the smaller force is $F$

so bigger force is $2F$

resultant $\left(R\right)=2F$

$R^2=F^2+{\left(2F\right)}^2+2\times F\times 2F\cos \left(x\right)$ (its a formula)

$\begin{array}{c}4F^2=F^2+4F^2+4F^2\cos \left(x\right)\\ 4F^2\cos \left(x\right)=F^2\\ \cos \left(x\right)=\frac{-1}{4}\\ x={\cos }^{-1}\left(\frac{-1}{4}\right)\end{array}$

$\therefore$ Option $D$ is correct.