Question

A force is resolved into components$P$ and $Q$ equally inclined to it. Then,

• A. $P=2Q$
• B. $2P=Q$
• C. $P=Q$
• D. NONE

Answer 1

The correct option is C

$P=Q$

Explanation for the correct option(s):

option C : $P=Q$

Since both component are equally aligned, $\alpha =45°$

$\begin{array}{rcl}P& =& F\cos \alpha \\ Q& =& F\sin \alpha \\ \frac{Q}{P}& =& \frac{F\sin \alpha }{F\cos \alpha }\\ \frac{Q}{P}& =& \tan \alpha \\ \frac{Q}{P}& =& \tan 45°\\ P& =& Q\end{array}$

Hence, option C is correct.