A block of mass $$10$$ kg is in contact against the inner wall of a hollow cylindrical drum of radius $$1$$ m. 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 $$g=10$$ $$m/s2$$

Question

A block of mass $$10$$ kg is in contact against the inner wall of a hollow cylindrical drum of radius $$1$$ m. 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 $$g=10$$ $$m/s2$$

Infinity Learn · Accepted Answer

To keep the block stationary,   Frictional force ≥ Weight  μN≥Mg  Here, $$N=M$$ω$$2r$$ $$r=1$$ m,μ$$=0.1$$  For minimum ω,μMω$$2r=Mg$$ ω$$=g$$μ$$r=100.1$$×$$1=10rads-1$$

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