First slide

Vectors

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

Moderate

A

2N
B

4N
C

6N
D

7N

Solution

$x + y = 16. A l s o, y^{2} = 8^{2} + x^{2} o r y^{2} = 64 + {(16 - y)}^{2} [x = 16 - y]$

$\begin{array}{l} o r y^{2} = 64 + 256 + y^{2} - 32 y \\ o r 32 y = 320 o r y = 10 N \\ \Rightarrow x + 10 = 16 o r x = 6 N \end{array}$

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