Question

Two horizontal forces of magnitudes $10N$ and $PN$ act on a particle. The force of magnitude $10N$ acts due west and the force of magnitude $PN$ acts on a bearing of ${30}^o$ east of north as shown in figure. The resultant of these two force acts due north. Find the magnitude of this resultant.

• A. $10\sqrt{3}N$
• B. $30\sqrt{3}N$
• C. $20\sqrt{3}N$
• D. $40\sqrt{3}N$

Answer 1

The correct option is A $10\sqrt{3}N$

The resultant force acts due north.

$\Rightarrow$ The horizontal components of the two forces cancel

$\Rightarrow$ $10=P\sin 30=\frac{P}{2}=10\Rightarrow P=20N$

$\therefore$ Resultant $R=P\cos 30=20\times \frac{\sqrt{3}}{2}=10\sqrt{3}N$.