Question

A $70\text{kg}$ man stands in contact against the inner wall of a hollow cylindrical drum of radius $3\text{m}$ rotating about its vertical axis. The coefficient of friction between the wall and his clothing is $0.15$. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

• A. $0.7\text{rad/s}$
• B. $4.7\text{rad/s}$
• C. $3.7\text{rad/s}$
• D. $14\text{rad/s}$

Answer 1

The correct option is B $4.7\text{rad/s}$

From FBD of man:


$N=mR{\omega }^2$ ... (i) and
$\mu N=mg$ ... (ii) (in limiting case i.e man just about to fall)
From (i) and (ii), we get
$\omega =\sqrt{\frac{g}{\mu R}}$
$=\sqrt{\frac{9.8}{0.15\times 3}}=4.7\text{rad/s}$