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Question

A road is 7.5 m wide and its outer edge is raised by 1.5 m over the inner edge. The radius of curvature is 50 m. If g=10 m/s2, for what speed of the car is this road suited?

A
2.5 m/s
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B
5 m/s
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C
10 m/s
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D
15 m/s
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Solution

The correct option is C 10 m/s
By the FBD of the car,
By balancing the vertical forces we get,
Ncosθ=mg ...(i) and here the horizontal component of the normal provides the necessary centripetal force.
Nsinθ=mv2r ...(ii), by dividing both the above equation (i) and (ii) we get,
tanθ=v2rg ...(iii)

For finding the angle θ,It is given in the problem that L=7.5 m and h=1.5.
Here we get sinθ=hL=1.57.5=15, for small angle θ we know that,
sinθ=tanθ=θ, by substituting this value in equation (iii) we get,
15=v2rgv2=rg5=50×105=10 m/s

Hence option C is the correct answer

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