Question

A light ladder is supported on a rough floor and leans against a smooth wall, touching the wall at height \( h \) above the floor. A man climbs up the ladder until the base of the ladder is on the verge of slipping. The coefficient of static friction between the foot of the ladder and the floor is \( \mu \). The horizontal distance moved by the man is:

• A. \( \mu^2 h \)
• B. \( \frac{\mu}{h} \)
• C. \( \mu h \)
• D. \( \mu^2 h^2 \)

Hint:

The distance moved by a person on a ladder depends on the frictional force and the height at which the ladder touches the wall.

Answer 1

The Correct Option is C

In this case, the condition for slipping at the base of the ladder is when the frictional force equals the horizontal force. The torque about the base of the ladder will balance at the verge of slipping. The equation for the static friction force is: \[ f_{\text{friction}} = \mu \cdot N \] where \( N \) is the normal force. The horizontal force and the weight of the man on the ladder create a torque that balances out, and the horizontal distance moved by the man is given by: \[ d = \mu h \] Thus, the horizontal distance moved by the man is \( \mu h \).