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Physics · MOTION IN A PLANE
हिन्दीA force vector \( \mathbf{F} \) of magnitude 50 N is resolved into two non-orthogonal component vectors making angles of \( 30^\circ \) and \( 45^\circ \) on opposite sides of \( \mathbf{F} \). Calculate the magnitude of the component vector that makes an angle of \( 30^\circ \) with \( \mathbf{F} \).
Correct answer · Option 1
\( 50(\sqrt{3}-1)\text{ N} \)
Explanation
Applying the sine rule to the vector triangle: \( \frac{F}{\sin(180^\circ - 75^\circ)} = \frac{F_1}{\sin 45^\circ} \implies F_1 = 50 \times \frac{\sin 45^\circ}{\sin 75^\circ} = 50 \times \frac{1/\sqrt{2}}{\frac{\sqrt{3}+1}{2\sqrt{2}}} = \frac{100}{\sqrt{3}+1} = 50(\sqrt{3}-1)\text{ N} \).
