MCQ
Two forces of 10 N each are acting at an angle $\theta^{\circ}$ at a point. Their resultant force is 10 N . The value of $\theta$ will be.
- A$0^{\circ}$
- B$60^{\circ}$
- ✓$120^{\circ}$
- D$180^{\circ}$
✓
Answer
Correct option: C.
$120^{\circ}$
(C) Resultant force :
$\begin{aligned} F ^2 & = F _1^2+ F _2^2+2 F_1 F_2 \cos \theta \\ (10)^2 & =(10)^2+(10)^2+2 \times 10 \times 10 \times \cos \theta \\ 100 & =100+100+200 \cos \theta \\ -100 & =200 \cos \theta \\ \cos \theta & =-\frac{100}{200}=-\frac{1}{2}=\cos 120^{\circ}
\\ ∴\theta =120^{\circ}\end{aligned}$
Hence, option (C) is correct.
$\begin{aligned} F ^2 & = F _1^2+ F _2^2+2 F_1 F_2 \cos \theta \\ (10)^2 & =(10)^2+(10)^2+2 \times 10 \times 10 \times \cos \theta \\ 100 & =100+100+200 \cos \theta \\ -100 & =200 \cos \theta \\ \cos \theta & =-\frac{100}{200}=-\frac{1}{2}=\cos 120^{\circ}
\\ ∴\theta =120^{\circ}\end{aligned}$
Hence, option (C) is correct.
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