Question

A block of mass 10 kg in contact against the inner wall of a hollow cylindrical drum of radius 1m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be `(g=10 m//s^(2))`
A. `10pi rad//s`
B. `sqrt(10) rad//s`
C. `(10)/(2pi) rad//s`
D. `10 rad//s`

Answer 1

Correct Answer - D
To keep the block stationary

`muN=mg`
`N=(mg)/(mu)=(10xx10)/(0.1)=1000`
Block is rotating about its axis
`therefore N=(mv^(2))/(R) rArr V=sqrt((NR)/(m))=sqrt((1000xx1)/(10))=10 rad//sec`