Question

At what angle should be the two forces $2p$ and $\sqrt{2}p$ act so that the resultant force is $p\sqrt{10}$:

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$

Let $\theta$ be the angle between two forces.
so, ${\left(p\sqrt{10}\right)}^2={\left(2p\right)}^2+{\left(\sqrt{2}p\right)}^2+2\left(2p\right)\left(\sqrt{2}p\right)\cos \theta$
$10=4+2+4\sqrt{2}\cos \theta$

$4=4\sqrt{2}\cos \theta$

$\cos \theta =\frac{1}{\sqrt{2}}$

$\theta ={45}^o$