A ladder of length $l$ and mass $= m$ leans against a frictionless wall. The base of the ladder makes an angle $\theta$ with the rough floor, $\mu _ { s }$. Providing that the ladder is in static equilibrium, the relation between $\theta$ and $\mu _ { s }$ is
A) $2 \mu \tan \theta = 1$
B) $2 \mu = m g \cos \theta$
C) $\mu = 2 \theta$
D) $\tan \theta = \mu$

Question

Quizplus · Accepted Answer

For static equilibrium, the frictional force at the base must balance the horizontal component of the ladder's weight. The condition for no slipping is $\mu_s \geq \frac{1}{2} \tan \theta$, which simplifies to $2 \mu \tan \theta = 1$.

A Ladder of Length lll And Mass =m= m=m Leans Against a Frictionless Wall

A Ladder of Length $l$ And Mass $= m$ Leans Against a Frictionless Wall