Question

If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it in direction, find the other component using vector method. If p is horizontal force.

• A. $Q=P\sqrt{3}$
• B. $Q=P\sqrt{2}$
• C. $Q=2P\sqrt{2}$
• D. $Q=2P\sqrt{3}$

Answer 1

Answer: (B)

$Q=P\sqrt{2}$

Let $P$ be horizontal in the direction of unit vector $i$.

The resultant is also $P$ but perpendicular to it in the direction of unit vector $j$.
If $Q$ be the other force making an angle $\theta$ (obtuse) as resultant is perpendicular to $P$,

then the two forces are $Pi$ and $\cos \theta i+Q\sin \theta j.$

Their resultant is $Pj$.
$\therefore Pj=Pi+(Q\cos \theta i+Q\sin \theta j)$
Equating the coefficients of $i$ and $j$, we get $P+Q\cos \theta =0$ and $P+Q\sin \theta =P.$
or $Q\cos \theta =-P$ and $Q\sin \theta =P$
Squaring and adding $Q=P\sqrt{2}$