Question

The horizontal force and the force inclined at an angle $60^{o}$ with the vertical, whose resultant is in vertical direction of

P kg, are

• A. P, 2P
• B. $P,P\sqrt{3}$
• C. $2P,P\sqrt{3}$
• D. None of these

Answer 1

Answer: (C)

$2P,P\sqrt{3}$

Answer 2

Let $\overset{\rightarrow}{OA} = P_{1}\mathbf{i},$ $\overset{\rightarrow}{CB} = - P_{1}\mathbf{i},$ $\overset{\rightarrow}{OB} = - P_{1}\mathbf{i} + P\mathbf{j}$

$\frac{\overset{\rightarrow}{OB}.j}{OB} = \cos 60{^\circ} \Rightarrow \frac{( - P_{1}i + Pj).j}{\sqrt{P_{1}^{2} + P^{2}}} = \frac{1}{2}$

$\Rightarrow 2P = \sqrt{P^{2} + P_{1}^{2}} \Rightarrow P_{1} = P\sqrt{3}$

$|\overset{\rightarrow}{OB}| = \sqrt{P^{2} + P_{1}^{2}} = \sqrt{P^{2} + 3P^{2}} = 2P.$