Question

Two forces of same magnitude 'F' are at right angles to each other. What is the magnitude of the total force acting on the object?​

Answer 1

Answer:

$\sqrt{2}$ F

Explanation:

Heya friend ,

Here we go :

For finding the resultant force, we can use the formula -

$F_{resultant}$ = $\sqrt{F_{1}^{2} + F_{2}^{2} + 2F_{1} F_{2} cos\alpha }$                    (for simplicity, I have taken $\alpha$ )

where, $\alpha$ is the angle between the 2 forces.

and,

$F_{1} = F_{2} = F$  

and

$\alpha$ = 90°

So,

$F_{resultant} = \sqrt{F^{2} + F^{2} + 2FFcos90}$

and,

cos 90° = 0

Hence,

$F_{resultant} =\sqrt{2F^{2} }$

               = $\sqrt{2}$ F

Thanks !

@Manav