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Question

A car is travelling on a track which has radius of curvature 50 m. What is the maximum safe speed with which the car can travel on this track? Take g=10 m/s2. Assume coefficient of friction to be 0.8.

A
103 m/s
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B
10 m/s
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C
20 m/s
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D
105 m/s
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Solution

The correct option is C 20 m/s
In this case, the track is not banked, so component of normal is not available to support the requirement of centripetal force along the curve.
The only reliability is on the frictional force between the track and wheels of car


Applying equation of circular dynamics on car:
N=mg ......(i) and
f=mv2r .......(ii)

Since we are asked for maximum safe velocity, we should consider limiting friction i.e fmax=μN .....(iii)

So, combining Eq.(i), (ii), (iii):
mv2maxr=μ×(mg)
Putting r= 50 m,
vmax=μgr=0.8×10×50=20 m/s

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