The sum of the magnitudes of two forces acting at a point is $$16$$ N. The resultant of these forces is perpendicular to the smaller force and has a magnitude of $$8$$ N. If the smaller force is of magnitude x, then the value of x is

Question

The sum of the magnitudes of two forces acting at a point is $$16$$ N. The resultant of these forces is perpendicular to the smaller force and has a magnitude of $$8$$ N. If the smaller force is of magnitude x, then the value of x is

Infinity Learn · Accepted Answer

x $$+$$ y $$=16$$.           Also, $$y2=$$ $$82+$$ $$x2$$           or       $$y2=$$ $$64$$ $$+$$ $$16$$ − $$y2$$     [ x $$=$$ $$16$$ − y] or       $$y2=$$ $$64$$ $$+$$ $$256$$ $$+y2$$− $$32y$$           or       $$32y$$ $$=$$ $$320$$      or       y $$=$$ $$10$$ N           ⇒   x $$+$$ $$10$$ $$=$$ $$16$$ or x $$=$$ $$6N$$

The sum of the magnitudes of two forces acting at a point is 16 N. The resultant of these forces is perpendicular to the smaller force and has a magnitude of 8 N. If the smaller force is of magnitude x, then the value of x is

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