Answer
a) $\tau=+FL$
b) $\tau=+FL$
c) $\tau=+FL$
Work Step by Step
a) When the axis passes through point A, only force $\vec{F}$ produces torque. The lever arm is $L/2+L/2=L$
Since the rotation is counterclockwise, $\tau\gt0$ $$\tau=+FL$$
b) When the axis passes through point B, both forces $\vec{F}$ and $-\vec{F}$ produce torque. The lever arm for both forces is $L/2$.
Since the rotation is counterclockwise, $\tau\gt0$ $$\tau=+\Big(\frac{FL}{2}+\frac{FL}{2}\Big)=+FL$$
c) When the axis passes through point C, only force $-\vec{F}$ produces torque. The lever arm is $L/2+L/2=L$
Since the rotation is counterclockwise, $\tau\gt0$ $$\tau=+FL$$
