Question

A hollow cylinder of radius r rotates about its axis with a frequency f such that a person on the wall does not fall. The minimum value of coefficient of friction is

(A) \(\frac{4\pi^2f^2r}g\)

(B) \(\frac{f^2r}g\)

(C) \(\frac{\pi^2f^2r}g\)

(D) \(\frac g {4\pi^2f^2r}\)

Answer 1

Correct option is (D) \(\frac g {4\pi^2f^2r}\)

frequency = f

So, µN = mg

N = mw²R

µmw²R = mg

µw²R = g

\(\frac w{2\pi } \) = f

w = 2πf

µ = \(\frac g {4\pi^2f^2r}\)