A hollow vertical cylinder of radius R is rot | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For the mass $M$ to remain suspended on the inner wall of the rotating cylinder,the upward frictional force $f_s$ must balance the downward gravit

Vedclass · Accepted Answer

$\mu = \frac{g}{\omega^2 R}$

Vedclass · Answer

(D) For the mass $M$ to remain suspended on the inner wall of the rotating cylinder,the upward frictional force $f_s$ must balance the downward gravitational force $mg$.$f_s \geqslant mg$Since the frictional force $f_s = \mu N$,where $N$ is the normal force provided by the wall of the cylinder,we have:$\mu N \geqslant mg$The normal force $N$ provides the necessary centripetal force for the mass $M$ to move in a circle of radius $R$ with angular velocity $\omega$:$N = M R \omega^2$Substituting this into the inequality:$\mu (M R \omega^2) \geqslant Mg$$\mu \geqslant \frac{g}{R \omega^2}$Therefore,the minimum coefficient of static friction is:$\mu_{\min} = \frac{g}{R \omega^2}$

$A$ hollow vertical cylinder of radius $R$ is rotated with angular velocity $\omega$ about an axis through its center. What is the minimum coefficient of static friction necessary to keep the mass $M$ suspended on the inside of the cylinder as it rotates?

Similar Questions

$A$ car moves along a circular track of radius $R$ banked at an angle of $30^o$ to the horizontal. The coefficient of static friction between the wheels and the track is $\mu$. The maximum speed with which the car can move without skidding out is

$A$ coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table is halved,it will just slip when placed at a distance of $............\,cm$ from the center.

$A$ bike moving at a speed of $60 \; km/hr$ takes a turn with a radius of $0.1 \; km$. At what angle with the vertical should the bike be tilted to avoid slipping?

$A$ car of mass $800 \, kg$ moves on a circular track of radius $40 \, m$. If the coefficient of friction is $0.5$,then the maximum velocity with which the car can move is ......... $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module