Question

In $x-y$ plane, a force $10N$ acts at an angle ${30}^{\circ }$ to the positive direction of $x$ axis. The force can be written as force needed is

• A. $5\hat{i}+5\hat{j}$
• B. $5\hat{i}+5\sqrt{3}\hat{j}N$
• C. none of these
  
• D. $5\sqrt{3}\hat{i}+5\hat{j}N$

Answer 1

The correct option is D $5\sqrt{3}\hat{i}+5\hat{j}N$

Let, $\overrightarrow{F}=x\hat{i}+y\hat{j}$
Now, $F=\sqrt{x^2+y^2}=10$
$\Rightarrow x^2+y^2=100\dots \left(i\right)$
$tan{30}^{\circ }=\frac{y}{x}\Rightarrow y=\frac{1}{\sqrt{3}}x.....\left(\dot{ii}\right)$
Solving $\dot{\left(i\right)}$ and $\dots \left(ii\right)$
$y=5N,x=5\sqrt{3}N$
Final Answer : $\left(b\right)$