Question

The resultant of two equal forces acting at right angles to each other is $1414$ dyne. Find the magnitude of either force.

• A. $960$
• B. $1000$
• C. $1200$
• D. $1414$

Answer 1

The correct option is B $1000$

Given,

$F_1=F_2=F\left(say\right)$

$\theta ={90}^0$

$R=1414dyne$

Resultant force,

$R=\sqrt{F_1^2+F_2^2+2F_1{F}_{2}cos\theta }$

$1414dyne=\sqrt{F^2+F^2+2F^{2}cos{90}^0}=\sqrt{2F^2}$

$1414dyne=\sqrt{2}F$

$F=\frac{1414}{\sqrt{2}}=999.84\approx 1000dyne$ (by rounding off)

The correct option is B.