Question

If $F_1=5\text{N}$ and $F_2=10\text{N}$ as shown in the figure, the resultant $R$ will be [Hint: $\cos {65}^{\circ }=0.423$]

• A. $14.93\text{N}$
• B. $15.93\text{N}$
• C. $10.93\text{N}$
• D. $12.93\text{N}$

Answer 1

The correct option is D $12.93\text{N}$

From the question, the angle between the force vectors is
$\theta ={90}^{\circ }-{15}^{\circ }-{10}^{\circ }={65}^{\circ }$
Therefore, resultant is
$R=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos \theta }$
$\Rightarrow R=\sqrt{5^2+{10}^2+2\times 5\times 10\times \cos {65}^{\circ }}$
$\Rightarrow R=\sqrt{25+100+100\times 0.423}=12.93\text{N}$