Question

The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is:

• A. ${120}^0$
• B. ${135}^0$
• C. ${90}^0$
• D. ${150}^0$

Answer 1

The correct option is A ${120}^0$

Lets consider two forces $F_1$ and $F_2$ are given.

$R=$ resultant of two forces

According to question,

$|F_1|=2|F_2|$

$\overrightarrow{R}={\overrightarrow{F}}_1+{\overrightarrow{F}}_2$. . . . . . . . .(1)

Resultant $R$ is perpendicular to to the smaller force.

$\overrightarrow{R}.{\overrightarrow{F}}_2=0$

$({\overrightarrow{F}}_1+{\overrightarrow{F}}_2).{\overrightarrow{F}}_2$

${\overrightarrow{F}}_1.{\overrightarrow{F}}_2+{\overrightarrow{F}}_2.{\overrightarrow{F}}_2=0$

$|{\overrightarrow{F}}_1||{\overrightarrow{F}}_2|cos\theta +|F_2{|}^2=0$

$2|F_2||F_2|cos\theta +|F_2{|}^2=0$

$2cos\theta +1=0$

$cos\theta =-\frac{1}{2}$

$\theta =co{s}^{-1}(-0.5)$

$\theta ={120}^0$

The correct option is A.