Vector Algebra Question 319
Question: If the resultant of two forces of magnitudes P and Q acting at a point at an angle of $ 60^{o} $ is $ \sqrt{7}Q, $ then P/Q is
[Roorkee 1999]
Options:
A) 1
B) $ \frac{3}{2} $
C) 2
D) 4
Show Answer
Answer:
Correct Answer: C
Solution:
- $ R^{2}=P^{2}+Q^{2}+2PQ\cos \theta $
Þ $ {{(\sqrt{7}Q)}^{2}}=P^{2}+Q^{2}+2PQ\cos 60{}^\circ $
Þ $ 7Q^{2}=P^{2}+Q+PQ $
Þ $ P^{2}+PQ-6Q^{2}=0 $
Þ $ P^{2}+3PQ-2PQ-6Q^{2}=0 $
Þ $ P(P+3Q)-2Q(P+3Q)=0 $
Þ $ (P-2Q)(P+3Q)=0 $
Þ $ P-2Q=0 $ or $ P+3Q=0 $ From $ P-2Q=0 $
Þ $ \frac{P}{Q}=2 $ .
BETA
