Question

Two equal forces ($P$ each) act at a point inclined to each other at an angle of $120°$. The magnitude of their resultant is

• A. $\frac{P}{2}$
• B. $\frac{P}{4}$
• C. $P$
• D. $2P$

Answer 1

The correct option is C

$P$

Step 1:Given;

$$\begin{gathered} F_1=F_2=P \\ \theta =120° \end{gathered}$$

Step 2: Formula used;

Resultant force $F_R=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos \theta }$

Step 3: Find the magnitude of their resultant;

$$\begin{gathered} F_R=\sqrt{P^2+P^2+2P^2\cos 120°} \\ \Rightarrow F_R=\sqrt{2P^2+2P^2(-0.5)} \\ \Rightarrow F_R=\sqrt{2P^2-P^2} \\ \Rightarrow F_R=P \end{gathered}$$

Hence, the magnitude of their resultant is $P$.

Thus, option C is correct.