Question

Out of the following pairs of forces, the resultant of which cannot be 4 newton is:

• A. 2 newton and 2 newton
• B. 2 newton and 4 newton
• C. 2 newton and 6 newton
• D. 2 newton and 8 newton

Answer 1

The correct option is D 2 newton and 8 newton

Let $\theta$ be angle b/w two vectors. $\left|A\right|=2\left|B\right|=8$

their resultant has magnitude

$\left|R\right|=\sqrt{A^2+B^2+2AB\cos \theta }$ or ${\left|R\right|}^2=A^2+B^2+2AB\cos \theta$

$\Rightarrow \frac{{\left|R\right|}^2-\left(90\right)}{32}=\cos \theta$ Now if $\left|R\right|=4$

$\frac{16-70}{32}=\cos \theta =-1.68$, which is not possible.

$\Rightarrow \left|A\right|=2$ and $\left|B\right|=8$ can never add up to give $\left|R\right|=4$.