Question

Forces of $1,2$unit act along the lines $x=0$ and $y=0$. The equation of the line of action of the resultant is

• A. $y–2x=0$
• B. $2y–x=0$
• C. $y+x=0$
• D. $y–x=0$

Answer 1

The correct option is B

$2y–x=0$

Step 1. Given data:

The first force, $F_1=1unit$, acts along $y$ axis

The second force, $F_2=2unit$ acts along $x$axis

Step 2. Resultant equation

According to given question, the resultant force is in direction $(2,1)$ with respect to origin

the points are,

$$\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(2,1) \end{gathered}$$

The slope is,

$$\begin{gathered} \frac{y_2-y_1}{x_2-x_1}=slope=m \\ \frac{1-0}{2-0}=m \\ \Rightarrow m=\frac{1}{2} \end{gathered}$$

The equation of line is,

$$\begin{gathered} y-y_1=m\left(x-x_1\right) \\ \Rightarrow y-0=\frac{1}{2}\left(x-0\right) \\ \Rightarrow 2y-x=0 \end{gathered}$$

Hence, option B is correct