Question

Two forces each numerically equal to 10 dynes are acting as shown in the following figure, then their resultant is

• A. $10$ dynes
• B. $20$ dynes
• C. $10\sqrt{3}$ dynes
• D. $5$ dynes

Answer 1

The correct option is A $10$ dynes

$\text{Step 1: Represent the two vectors graphically [Refer Fig.]}$

$F_1=F_2=10dynes$

Join the tail of both vectors then angle between $F_1$ and $F_2$

$\varphi =180-{60}^{\circ }$

$={120}^{\circ }$

$\text{Step 2: Resultant}$

$R=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos \varphi }$

$=\sqrt{{10}^2+{10}^2+2(10\times 10)\cos 120}$

$=\sqrt{{10}^2}$

$R=10dynes$

Hence option $A$ is correct