Question

If the resultant of two forces of magnitude p and 2p is perpendicular to p, then the angle between the forces is

Moderate

Solution

$tanα = \frac{2 psinθ}{p + 2 pcosθ}; here α = 90^{0}$
$\Rightarrow \infty = \frac{2 psinθ}{p + 2 pcosθ} \Rightarrow p + 2 pcosθ = 0$
$\Rightarrow cosθ = - \frac{1}{2} \Rightarrow θ = \frac{2 π}{3}$

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