Question

A ladder of length $L$ leans against a wall at an angle of $\theta$ from the horizontal, as shown in figure. The normal force $F_N$ applied from the ground on the ladder applies what torque about the ladders centre of mass?

• A. $F_{N}L/2$
• B. $F_{N}L\cos \theta$
• C. $F_{N}L\sin \theta$
• D. $F_{N}L/2\cos \theta$

Answer 1

The correct option is D $F_{N}L/2\cos \theta$

The direction of normal force is shown in the shown in the attached figure. It has two components $F_N\sin \theta$ along the ladder and $F_N\cos \theta$ perpendicular to the rod. Torque is defined as moment of force. Hence, torque is given by:

$\tau =F_N\cos \theta L/2$