Question

Two forces whose magnitudes are in the ratio of $3:5$, gives a resultant of $35N$. If the angle between them is ${60}^o$, then the magnitude of each force is

• A. $3N,5N$
• B. $9N,25N$
• C. $15N,25N$
• D. $21N,35N$

Answer 1

Answer: (C)

$15N,25N$

Using cosine law and assuming the forces to be of magnitudes $3x$ and $5x$,
$c=\sqrt{a^2+b^2+2abcos\theta }$
$35=\sqrt{34x^2+15x^2}$
therefore $x=35/7=5$.
Forces are thus equal to $15N$ and $25N$.