Question

There are two forces each having same magnitude $10\text{N}\text{.}$ One is inclined at an angle of $30^o$ and other is inclined at an angle of $135^{\text{o}}$ to the positive direction of $x$ -axis. The $x$ and $y$ components of the resultant are

• A. $1.59\text{N}\hat{i}$ and $12.07\text{N}\hat{j}$
• B. $10\text{N}\hat{i}$ and $10\text{N}\hat{j}$
• C. $1.59\text{N}\hat{i}$ and $10\text{N}\hat{j}$
• D. $1.59\text{N}\hat{i}$ and $2\text{N}\hat{j}$

Answer 1

Answer: (A)

After resolving forces in $xy-$ direction, we get
Along $x$ direction, net force;
$F_x=10\left[cos{\left(30\right)}^o+\left(-cos{\left(45\right)}^o\right)\right]=10\left(\frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}\right)=1.59\text{N}$
Along $y$ direction, net force;
$F_y=10\left(\text{sin}{\left(30\right)}^o+10\text{sin}{\left(45\right)}^o\right)$
$F_y=10(\frac{1}{2}+\frac{1}{\sqrt{2}})$
$=12.07N$
Thus forces in $x$ and $y$ direction are $1.59\text{N}$ and $12.07\text{N}$ respectively.