Question

Two equal forces ($P$ each) act at a point inclined to each other at an angle of ${120}^{\circ }$. The magnitude of their resultant is $\mu P$. Find $\mu$.

Answer 1

Given, two equal forces, $P=Q=P$

And angle between the two forces,

$\theta ={120}^{\circ }$

And resultant of these two forces,

$R=\mu P$

So, resultant of these two forces,

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

$\mu P=\sqrt{P^2+P^2+2PP\cos {120}^{\circ }}$

$\Rightarrow \mu P=P$

$\Rightarrow \mu =1$

Final answer: 1