Question

The greatest and the least resultant of two forces acting at a point are $10\text{N}$ and $6\text{N}$, respectively. If each force is increased by $3\text{N}$ and are acting at a point making an angle of ${90}^o$ with each other. Find the resultant of new forces.

• A. $\sqrt{146}\text{N}$
• B. $\sqrt{124}\text{N}$
• C. $\sqrt{188}\text{N}$
• D. $\sqrt{114}\text{N}$

Answer 1

The correct option is A $\sqrt{146}\text{N}$

Let $\overrightarrow{a},\overrightarrow{b}$ be two vectors of magnitudes $a,b$
Given,
$a+b=10$
$a-b=6$
Adding the equations $2a=16$
$\Rightarrow a=8,b=2$
Now magnitude of each vector is increased by $3\text{N}$
$a_1=a+3=11\text{N}$
$b_1=b+3=5\text{N}$
Given that new vectors act at ${90}^o,$ so resultant is
$R=\sqrt{a_1^2+b_1^2+2a_1{b}_{1}cos{90}^o}$
$R=\sqrt{{11}^2+5^2}=\sqrt{146}\text{N}$