A car is travelling on a track which has radius of curvature 50m. What is the maximum safe speed with which the car can travel on this track? Take g=10m/s2. Assume coefficient of friction to be 0.8.
A
10√3m/s
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B
10m/s
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C
20m/s
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D
10√5m/s
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Solution
The correct option is C20m/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=50m, vmax=√μgr=√0.8×10×50=20m/s