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3-1.Vectors
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Two forces, ${F_1}$ and ${F_2}$ are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is
A
${\cos ^{ - 1}}(1/2)$
B
${\cos ^{ - 1}}( - 1/2)$
C
${\cos ^{ - 1}}( - 1/4)$
D
${\cos ^{ - 1}}(1/4)$
Solution
(c)Let $F 1=F$
and $\quad F 2=2 F$
Resultant force $=F_{\text {net }}=2 F$
$F_{net}$ $=\sqrt{F_{1}^{2}+F_{2}^{2}+2 F_{1} F_{2}} \cos \theta$
$2 F=\sqrt{F^{2}+2 F^{2}+2 \times F \times(2 F) \cos \theta}$
$4 F^{2}=5 F^{2}+4 F^{2} \cos \theta$
$4 \cos \theta=-1$
$\therefore \cos \theta=\frac{-1}{4}$
Standard 11
Physics
