Question

The square of resultant of two equal forces is three times their product. Angle between the forces is

• A. $\pi$
• B. $\pi /2$
• C. $\pi /4$
• D. $\pi /3$

Answer 1

The correct option is D

$\pi /3$

Step 1: Given Data:

Let two forces are $F_1$ and $F_2$ and ${\displaystyle \theta }$ be the angle between them where the resultant is ${\displaystyle R}$

It is given that, the two forces are equal that is

$F_1=F_2$

The resultant is given as-

$R^2=3F_1{F}_2$

Step 2: Formula Used:

The resultant is given by

$R^2=F_1^2+F_2^2+2F_1{F}_2\cos \theta \dots \dots \dots \dots \dots \dots \dots \dots \left(1\right)$

Step 3: Calculation of the angle between the forces:

The net force can be calculated using the formula in equation (1)

Let $F_1=F_2=F$ and it is given that, $R^2=3F_1{F}_2$

$\begin{array}{rcl}{R}^2& =& F_1^2+F_2^2+2F_1{F}_2\cos \theta \\ 3F_1{F}_2& =& F_1^2+F_2^2+2F_1{F}_2\cos \theta \\ 3F^2& =& 2F^2+2F^2\cos \theta \\ F^2& =& 2F^2\cos \theta \\ \cos \theta & =& \frac{1}{2}\\ \theta & =& \frac{\mathrm{\pi }}{3}\end{array}$

Hence option D is the correct answer.