Question

Forces $F_1$ and $F_2$act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be

• A. $F_1+F_2$
• B. $F_1–F_2$
• C. $\sqrt{{F_1}^2+{F_2}^2}$
• D. ${F_1}^2+{F_2}^2$

Answer 1

The correct option is C

$\sqrt{{F_1}^2+{F_2}^2}$

Step 1 : Given data

Here have two forces $F_1$ and $F_2$ acting mutual perpendicular direction on a point mass.

Step 2 : To find the force

We know that the resultant

$$\begin{gathered} R=\sqrt{A^2+B^2+2AB\cos \theta } \\ R=\sqrt{{F_1}^2+{F_2}^2+2F_1{F}_2\cos 90} \\ \left(\cos 90=0\right) \end{gathered}$$

Therefore

$R=\sqrt{{F_1}^2+{F_2}^2}$

Hence the resultant force is $\sqrt{{F_1}^2+{F_2}^2}$

Therefore Option C is the correct answer