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Question

A car is moving on a circular level road of radius of curvature 300 m. If the coefficient of friction is 0.5 and taking g=10 m/s2, the maximum speed the car can have (in km/hr) is

A
278.9 km/h
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B
0.45 km/h
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C
139.4 km/h
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D
1 km/h
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Solution

The correct option is C 139.4 km/h
FBD of car:

Given,
Radius of curvature (r)=300 m
Coefficient of friction (μ)=0.5

N=mg i.e forces are balanced in vertical direction.
Along the radial direction, we have
f=mv2r i.e friction provides the centripetal force.
f=μN=μmg (limiting condition, when the car has maximum velocity and is just about to slip)
i.e μmg=mv2maxr
vmax=μrg
=0.5×300×10=38.72 m/s
=139.4 km/h

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