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
Text Solution
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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)
\(\tan \varphi = \frac{Q \sin \theta}{P + Q \cos \theta} = \tan 90^\circ = \infty\)
\(P + Q \cos \theta = 0\) .......(iii)
By solving (i), (ii) and (iii) we will get P = 5, and Q = 13
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