A car is moving on a circular level road of radius of curvature 300m. If the coefficient of friction is 0.5 and taking g=10m/s2, the maximum speed the car can have (in km/hr) is
A
278.9km/h
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B
0.45km/h
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C
139.4km/h
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D
1km/h
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Solution
The correct option is C139.4km/h FBD of car:
Given,
Radius of curvature (r)=300m
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=38.72m/s =139.4km/h