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Grade 11General Physics

Can two forces of magnitude 6N and 10N respectively have a resultant of (a). 12N (b). 18N ?

Anmol chaudhary

9 Years agoGrade 11

1 Answer

Shreya D Nanda

Approved Tutor Answer9 Years ago

Magnitude of resultant force is given by, $F_{r} =\sqrt{F_{1}^{2} +F_{2}^{2} +2F_{1}F_{2} \cos \theta }$

According to the given question, let us consider

12N as answer

$\therefore 12 = \sqrt{6^2 + 10^2 + 2*6*10 \cos \theta }$ $\Rightarrow 12=\sqrt{36+100+120\cos\theta }$

or $12^2=136+120\cos\theta$ $\Rightarrow \cos\theta = [144-136]/120 = 0.667$

$\Rightarrow \theta = 86.177^{\circ}$

$\therefore$ The answer to the question is 12N. , i.e, the resultant of forces 6N and 10N can be 12N when angle between the two forces is $\cos^{-1}0.667$ or $86.1774^{\circ}$ .

NOTE: The resultant of 6N and 10N can never be 18 N, as from above method, we get $\cos \theta = 1.556$

which is impossible becoz, $-1\leq \cos \theta \leq 1$

Hope you understand....

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