Question

In the XOY coordinate plane P(a, a) is a point. Two forces each of magnitude F are acting at P in the positive X-direction and positive Y-direction. The magnitude of the torque due to the forces about the origin is

• A. 2Fa
• B. zero
• C. $\sqrt{2}Fa$
• D. $Fal\sqrt{2}$

Answer 1

The correct option is B zero

The resultant of the forces acting on $P(a,a)$ is:

$\sqrt{F^2+F^2}=\sqrt{2}F$.(As the two forces are perpendicular to each other) The direction of resultant force is along the bisector of the angle made by the two forces, so it can be extended to pass through the origin $(0,0)$. so perpendicular distance from $(0,0)$ to $F_{net}=0$

Hence Torque$\left(\tau \right)=$ Force$\times$ perpendicular distance $=\sqrt{2}F\times 0=0$.