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Q.

In a certain machine at a fun fair, a man stands against the wall of a circular room of radius 3 m. The room rotates about a vertical axis through the centre of the floor at 2 rad/sec., then the floor is lowered- If the man does not slip vertically downwards, the least value of the coefficient of friction between the man and wall is

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a

g/ω2r

b

g/ωr

c

g2/ωr

d

g/ωr2

answer is A.

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Detailed Solution

When the machine rotates. the man also rotates with the wall. The contact force R between the wall and man is centripetal force. Due to this contact force R, there is frictional force µ R. The upward frictional force is balanced by weight of the man. HenceR=mv2r= mω2rand Î¼R=mgμmω2r=mg  or  Î¼=gω2r.
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In a certain machine at a fun fair, a man stands against the wall of a circular room of radius 3 m. The room rotates about a vertical axis through the centre of the floor at 2 rad/sec., then the floor is lowered- If the man does not slip vertically downwards, the least value of the coefficient of friction between the man and wall is