A force has magnitude 20N. Its one rectangular component is 12N, the other rectangular component must be:

8 N

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14 N

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16 N

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32 N

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Solution

The correct option is C 16 N
By rectangular component,
the two forces $F_{1} (12 N)$ and $F_{2}$ are perpendicular forces with resultant as $20 N$
Using Pythagorus theorem
$R^{2} = F_{1}^{2} + F_{2}^{2} 20^{2} = 12^{2} + F_{2}^{2} 400 = 144 + F_{2}^{2} F_{2}^{2} = 400 - 144 F_{2}^{2} = - 256 F_{2} = 16 N$

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