The maximum and minimum magnitudes of the resultant of two forces are 17 newton and 7 newton respectively, if these two forces are acting at right angle to each other, then the value of resultant of these forces in newton will be:

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Solution

The correct option is C 13
$| F_{m a x} | = 17 N \Rightarrow F_{1} + F_{2} = 17$
$| F_{m i n} | = 7 N \Rightarrow F_{1} - F_{2} = 7$
$\Rightarrow F_{1} = 12 N$ and $F_{2} = 5 N$
When, $θ = 90^{0}$
$F_{r e s u l t a n t} = \sqrt{F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} C o s θ}$
$= \sqrt{12^{2} + 5^{2} + 0} = 13 N$

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The maximum and minimum magnitudes of the resultant of two forces are 17 newton and 7 newton respectively, if these two forces are acting at right angle to each other, then the value of resultant of these forces in newton will be:

The correct option is C 13|Fmax|=17 N⇒F1+F2=17|Fmin|=7 N⇒F1−F2=7⇒F1=12N and F2=5NWhen, θ=900Fresultant=√F21+F22+2F1F2Cosθ =√122+52+0=13N