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Question

A motorcyclist of mass 100 kg is moving in a horizontal circle inside a hollow cylinder of radius 50 m. The coefficient of friction between the tires of the motorcycle and the surface of the hollow cylinder is 0.8. Then, the minimum speed with which he should ride the motorcycle to keep moving in a horizontal circle is

A
25 m/s
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B
0.5 m/s
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C
50 m/s
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D
2.5 m/s
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Solution

The correct option is A 25 m/s
FBD of the motorcycle:

N=mRω2... (1)
fs=mg... (2)

From (1) and (2)
fsN=gRω2
Since fsμsN, we get μsgRω2
ω2gμRωmin=gμR
As v=Rω,
vmin=RgμR=gRμ
=10×500.8=25 m/s

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