First slide

Scalars and Vectors

Question

A force of 1000 N in a particular direction must be applied to a block. For same reason. It is not possible to apply the force in that direction but two forces can be applied to 30^o and 45^o on either side of it in the same plane containing the given force. If the ratio of magnitude of forces as $\sqrt{n}$ The value of n is_______.

Moderate

Solution

The resultant of F₁ and F₂ is in direction of 1000 N force. So, the sum of component of F₁ and F₂ in perpendicular direction of 1000 N force will be zero.
$\begin{array}{l} ∴ F_{1} \sin 30^{\circ} = F_{2} \sin 45^{\circ} \\ or \frac{F_{1}}{F_{2}} = \frac{\sin 45^{\circ}}{\sin 30^{\circ}} = \frac{1}{\sqrt{2} \times \frac{1}{2}} = \sqrt{2} \\ ∴ n = 2 \end{array}$

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