Question

Two forces whose magnitudes are in a ratio 5 : 8 gives a resultant of magnitude of 49. If the angle between them is ${120}^o,$ then the magnitude of the two forces are

• A. 15 and 24
• B. 20 and 32
• C. 35 and 56
• D. 30 and 48

Answer 1

The correct option is C 35 and 56

Say, $A=5x$ and $B=8x$
$R=\sqrt{A^2+B^2-AB}=\sqrt{25x^2+64x^2-40x^2}=\sqrt{49x^2}$
$49=7x$
$x=7$
$\therefore A=5x=35andB=8x=56$