Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
1906 Upvotes
Verified Answer
The correct answer is:
$p$
The magnitude of the resultant force can be given by parallelogram's law of vector addition i.e.,
$$
\begin{aligned}
\Rightarrow \quad F_{\text {net }} &=\sqrt{2 p^{2}+2 p^{2} \times \cos \left(120^{\circ}\right)}\left(\because \theta=120^{\circ}\right) \\
&=\sqrt{2 p^{2}+2 p^{2}\left(-\frac{1}{2}\right)} \\
&=\sqrt{p^{2}} \\
&=p
\end{aligned}
$$
$$
\begin{aligned}
\Rightarrow \quad F_{\text {net }} &=\sqrt{2 p^{2}+2 p^{2} \times \cos \left(120^{\circ}\right)}\left(\because \theta=120^{\circ}\right) \\
&=\sqrt{2 p^{2}+2 p^{2}\left(-\frac{1}{2}\right)} \\
&=\sqrt{p^{2}} \\
&=p
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.