Kinematics Question 109

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

Show Answer

Answer:

Correct Answer: C

Solution:

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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