Vector Algebra Question 146
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
[IIT 1983]
Options:
A) $ P,2P $
B) $ P,P\sqrt{3} $
C) $ 2P,P\sqrt{3} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- Let $ \overrightarrow{OA}=P_1\mathbf{i}, $ $ \overrightarrow{CB}=-P_1\mathbf{i}, $ $ \overrightarrow{OB}=-P_1\mathbf{i}+P\mathbf{j} $ $ \frac{\overrightarrow{OB},.,j}{OB}=\cos 60{}^\circ \Rightarrow \frac{(-P_1i+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} $ $ |\overrightarrow{OB}|,=\sqrt{P^{2}+P_1^{2}}=\sqrt{P^{2}+3P^{2}}=2P. $
BETA
