Question

A person in contact with the inner wall of a vertical hollow cylinder of radius $1m$ remains in equilibrium without slipping down as the cylinder is rotated about its own vertical axis with an angular velocity $3.5rad/s$. The minimum coefficient of static friction between the person and the wall of the cylinder, such that the person does not slip is:

& A.0.2 \\\ & B.0.4 \\\ & C.0.6 \\\ & D.0.8 \\\ \end{aligned}$$

Answer 1

We know that friction is the resistive force which tries to oppose the motion of an object. It is a surface phenomenon and is observed only when the object trying to move is in contact with some surface. Which is to say that friction is a contact force.
Formula:
$\mu_{s}=\dfrac{F_{s}}{F_{n}}$

Complete answer:
Coefficient of static friction is a dimensionless quantity, $\mu_{s}$ is the maximum resistive force applied on any given body such that there is no change in state of the motion.
It is given as $\mu_{s}=\dfrac{F_{s}}{F_{n}}$, where $F_{s}$ is the applied force and $F_{n}$ is the normal force acting on the given body.
Here, given that the angular velocity of the cylinder with radius $r=1m$ is $\omega=3.5rad/s$. Let $m$ be the mass of the cylinder, then the normal force of the cylinder is given as $F_{n}=m\omega^{2} r$, also the applied force or the force due to gravity is given as $F_{s}=mg$.
Substituting, we get $\mu_{s}=\dfrac{mg}{m\omega^{2} r}=\dfrac{10}{3.5^{2}\times 1}= 0.8$

Hence the answer is $D.0.8$

Additional information:
Friction can be classified into three types broadly.
1. Static friction: is the friction experienced when one tries to move a body which is at rest, such that there is no friction between the body and the surface.
2. Kinetic friction: is the friction experienced when the object is in relative motion to the surface.
3. Normal friction: is a perpendicular component of the contact force. It is equal and opposite in direction to the gravitational force experienced by a body.

Note:
Friction is a small quantity that acts in the opposite direction to the force. Static friction is the force responsible for an object to be at rest, whereas the kinetic friction is the force that resists the motion of a moving body. Coefficient of static friction is a ratio and has no units. Coefficient of static friction depends on the weight of the object and nature of the surface.