Question

Three forces having magnitude $50\text{N}$ each acting at a point as shown in figure. If the angles between neighbouring forces are equal, then the resultant is

• A. $0\text{N}$
• B. $9.8\text{N}$
• C. $2\times 9.8\text{N}$
• D. $3\times 9.8\text{N}$

Answer 1

The correct option is A $0\text{N}$


Using triangle law of vector addition, we can say that the resultant vector is zero vector.

Alternate:


If we resolve the vectors in $x$ and $y$ directions respectively we get
net force in $x$ direction $\overrightarrow{F_x}=\left(50\cos {30}^{\circ }\right)\hat{i}+(-50\cos {30}^{\circ })\hat{i}=0$
Also, net force in $y$ direction
$\overrightarrow{F_y}=(50\sin {30}^{\circ }+50\sin {30}^{\circ })\hat{j}+(-50)\hat{j}=0$
So, magnitude of net resultant force is
$|{\overrightarrow{F}}_{net}|=\sqrt{{|\overrightarrow{F_x}|}^2+{|\overrightarrow{F_y}|}^2}=0$