Vectors Question 79
Question: The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the, magnitudes of forces
[Roorkee 1992; AIEEE 2002]
Options:
A) 12, 5
B) 14, 4
C) 5, 13
D) 10, 8
Correct Answer: C Let P be the smaller force and Q be the greater force then according to problem ? P + Q = 18 ……(i) $ R=\sqrt{P^{2}+Q^{2}+2PQ\cos \theta }=12 $ …….(ii) $ \tan \varphi =\frac{Q\sin \theta }{P+Q\cos \theta }=\tan 90=\infty $ \ $ P+Q\text{ cos}\theta =0 $ …….(iii) By solving (i), (ii) and (iii) we will get $ P=5, $ and $ Q=13 $
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BETA
