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Question

A car is moving on a levelled circular road of radius of curvature 300 m. If the coefficient of static friction is 0.3 and acceleration due to gravity is 10 ms−2, then maximum allowable speed for the car will be (in kmh−1)

A
30
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B
81
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C
108
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D
162
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Solution

The correct option is C 108
To avoid slipping, frictional force will act in a direction to provide the necessary centripetal force. i.e frictional force will act towards centre of circular curvature.
Here, f is magnitude of frictional force.
f=mv2maxr
μsmg=mv2maxr

Here, it is given that
r=300 m,μs=0.3,g=10 ms2
Applying the formula,
vmax=μsrg=0.3×300×10=30 ms1
Or, 30×185 kmh1=108 kmh1

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