Question

Two equal forces act at a point perpendicular to each other. If the resultant is 1414N, then magnitude of each force is

• A. $500N$
• B. $1000N$
• C. $1000\sqrt{2}N$
• D. $500\sqrt{2}N$

Answer 1

The correct option is B $1000N$

The resultant of two force is given by $F=\sqrt{A^2+B^2+2AB\cos \theta }$ where, A & B are two vectors & $\theta$ is the angle between them.

In the given question, $\overrightarrow{A}=\overrightarrow{B}$ & $\cos \theta =cos{90}^0=0$

Therefore, $F=\sqrt{A^2+A^2}$ $=\sqrt{2}A$ $=1414$

Solving this we get, $A=1000N$