Question

A force of 10N is resolved into the perpendicular components. If the first component makes 30${}^0$ with the force the magnitudes of the components are:

• A. 5N, 5N
• B. $5\sqrt{2}N,5N$
• C. $5\sqrt{3}N,5N$
• D. $10N,1\sqrt{3}N$

Answer 1

Answer: (C)

$5\sqrt{3}N,5N$

Given that the magnitude of force, $F=10N$

We know the rectangular components of a $\overrightarrow{A}$ are given by:

$A\cos \theta$ and $A\sin \theta$

Therefore, magnitude of the components of $\overrightarrow{F}$ will be $10\cos {30}^o$ and $10\sin {30}^o$

where, $\theta ={30}^o$ as given

By putting the value of $\cos {30}^o$ and $\sin {30}^o$ the components are $5\sqrt{3}N$ and $5N$.