Question

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 :

• A. 2 : 1
• B. 3 : $2\sqrt{2}$
• C. 3 : 2
• D. 3 : $\sqrt{2}$

Answer 1

The correct option is B 3 : $2\sqrt{2}$

Let the forces be $F^{\prime }$ and $3F$ acting on the particle as shown in the above figure

$F$ and $F^{\prime }$ are perpendicular.

Let the angle between $3F$ and $horizontal$ be $\theta$

We have :

$3F\sin \theta =F$

$sin\theta =1/3$

As the resultant force is in vertical direction net horizontal force shoud be $zero$

$3F\cos \theta =F^{\prime }$

$F^{\prime }=3F\times \frac{2\sqrt{2}}{3}$

$F^{\prime }=2\sqrt{2}F$

Ratio $=3:2\sqrt{2}$