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Q.

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 $90^{0}$ with the force of smaller magnitude, if magnitudes of forces are P, Q then find $(P^{2} + Q)$ ?

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answer is 38.

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Detailed Solution

Let P be the smaller force and Q be the greater force then according to problem-
$P + Q = 18$ ….(i)
$R = \sqrt{P^{2} + Q^{2} + 2 P Q \cos θ} = 12$ …(ii)
$\tan ϕ = \frac{Q \sin θ}{P + Q \cos θ} = \tan 90 = \infty$
$∴ P + Q \cos θ = 0$ …(iii)
By solving (i), (ii) and (iii) we will get $p = 5$ , and $Q = 13$

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