Question

A person is in contact with the inner wall of a vertical hollow cylinder of radius $2m$ without his feet touching the floor. He remains in equilibrium without slipping down when the cylinder is rotated about it's own vertical axis. If the coefficient of static friction between person and wall of cylinder is $0.4$, then the minimum angular velocity of cylinder should be:

• A. $1.5rad/s$
• B. $2rad/s$
• C. $3rad/s$
• D. $3.5rad/s$

Answer 1

The correct option is D $3.5rad/s$

For equillibrium
Max. Friction will balance $Mg$
$\therefore \mu N=Mg$ ----------- (1)
where $N=M{\omega }^{2}R$ ----------- (2)
$\mu M{\omega }^{2}R=Mg$
$\omega =\sqrt{\frac{g}{\mu R}}$
$=3.54rad/s$