The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one

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The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the other force. The ratio of larger force to smaller one is:

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![image](https://pub-7faa453bd1ec4bf0a04cc031c6f058de.r2.dev/images/c47958af-7f3e-4d89-b077-e657f08ad088.png) Let the forces be P and Q , where P is the larger force. Let R be perpendicular to Q .From the triangle of forces (or vector addition): P^2 = Q^2 + R^2 Given R = 1/3P . P^2 = Q^2 + (1/3P)^2 P^2 = Q^2 + 1/9P^2 Q^2 = P^2 - 1/9P^2 = 8/9P^2 Q = √(8/9) P = 2√(2)3 P The ratio of larger force ( P ) to smaller force ( Q ) is: P : Q = P : 2√(2)3 P = 1 : 2√(2)3 = 3 : 2√(2) .

The resultant $R$ of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the other force. The ratio of larger force to smaller one is:

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