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3.1 vectors — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.1 vectors1 Mark
MCQ
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
    ${\cos ^{ - 1}}( - 1/2)$
  • ✓
    ${\cos ^{ - 1}}( - 1/4)$
  • D
    ${\cos ^{ - 1}}(1/4)$
✓

Answer

Correct option: C.
${\cos ^{ - 1}}( - 1/4)$
c
(c)Let $F 1=F$

and $\quad F 2=2 F$

Resultant force $=F_{\text {net }}=2 F$

$F_{net}$ $=\sqrt{F_{1}^{2}+F_{2}^{2}+2 F_{1} F_{2}} \cos \theta$

$2 F=\sqrt{F^{2}+2 F^{2}+2 \times F \times(2 F) \cos \theta}$

$4 F^{2}=5 F^{2}+4 F^{2} \cos \theta$

$4 \cos \theta=-1$

$\therefore \cos \theta=\frac{-1}{4}$

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