Question

The resultant of two forces at right angle is $5N$ . When the angle between them is $120^o$ , the resultant is $\sqrt{13}N$ . Then the forces respectively are,

• A. $\sqrt{12}N,\sqrt{13}N$
• B. $\sqrt{20}N,\sqrt{5}N$
• C. $3\text{ N}\text{,}4\text{ N}$
• D. $\sqrt{40}N,\sqrt{15}N$

Answer 1

Answer: (C)

Let $A$ and $B$ be the two forces. As per question
$\sqrt{A^2+B^2}=5$
or $A^2+B^2=25$ ----------------------(i)
and $A^2+B^2+2ABcos120^{\circ }=13$
or $AB=25-13=12$
or 2 $AB=24$ ----------------------(ii)
Solving (i) and (ii), we get
$A=3\text{ N}$
and $B=4\text{ N}$