Question

The resultant of two forces at right angle is $5 \, N$ . 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 $B=4\text{ N}$