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

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
  1. $2: 1$
  2. $3: \sqrt{2}$
  3. $3: 2$
  4. $3: 2 \sqrt{2}$

Solution


$\mathrm{F}^{\prime}=3 \mathrm{~F} \cos \theta$ $\mathrm{F}=3 \mathrm{~F} \sin \theta$ $\Rightarrow \mathrm{F}^{\prime}=2 \sqrt{2} \mathrm{~F}$ $\mathrm{~F}: \mathrm{F}^{\prime}:: 3: 2 \sqrt{2}$.

Asked in: JEE Main 2005

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