Kinematics Question 444
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{}^\circ $ with the force of smaller magnitude, what are the magnitudes of forces?
Options:
A) 12, 5
B) 14, 4
C) 5, 13
D) 10, 8
Correct Answer: C [c] Let p be the smaller force and Q be the greater force then according to problem $ P _{i}+Q=18 $ … (i) $ R=\sqrt{P^{2}+Q^{2}+2PQ\cos \theta }=12 $ … (ii) $ \tan \phi =\frac{Q\sin \theta }{P+Q\cos \theta }=\tan 90^{o}=\infty $ $ \therefore $ $ P+Q\cos \theta =0 $ … (iii)
By solving Eqs. (i), (ii) and (iii) we will get $ P=5 $ and $ Q=13 $ .
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