A force of 12 N and another force of 5 N can be applied together to produce the effect of a single force Which of the following force can not be obtained :

14 N

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8 M

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18 M

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16 M

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Solution

The correct option is C 18 M
Given,
$F_{1} = 12 N$
$F_{2} = 5 N$
The resultant force, $R = \sqrt{F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} c o s θ}$ . . . . . . .(1)
For maximum force, $θ = 0^{0}$
$R_{m a x} = F_{1} + F_{2} = 12 N + 5 N = 17 N$
For minimum force, $θ = 180^{0}$
$R_{m i n} = F_{1} - F_{2} = 12 N - 5 N = 7 N$
So, from the above, the single force must be between $17 N$ to $7 N$ .
The correct option is C.

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