Question

A person with a mass of M kg stands in contact against the wall of a cylindrical drum of radius r rotating with an angular velocity w. If the coefficient of friction between the wall and the clothing is m, the minimum rotational speed of the cylinder which enables the person to remain stuck to the wall when the floor is suddenly removed is-

• A. w_min = $\sqrt{\frac{g}{\mu r}}$
• B. w_min = $\sqrt{\frac{\mu r}{g}}$
• C. w_min = $\sqrt{\frac{2g}{\mu r}}$
• D. w_min = $\sqrt{\frac{rg}{\mu}}$

Answer 1

Answer: (A)

w_min = $\sqrt{\frac{g}{\mu r}}$

Answer 2

mrw² = N and f = mg

but f £ mN \ mg £ mmrw²

w² ³ $\frac{g}{\mu r}$ \ w_min = $\sqrt{\frac{g}{\mu r}}$