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Question

A curve in a road forms an arc of radius 800 m If the road is 39.2 m wide, calculate the safe speed for turning, if the outer edge of the road is 0.5 m higher than the inner edge. Take g=9.8 m/s2.

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

The correct option is B 10 m/s
Here, radius of circular arc r=800 m, Distance between the edges of the road i.e AB=39.2 m
Height of the outer edge with respect to the inner edge h=0.5 m.


Applying the condition of banking, for maximum safe speed (v) :
tanθ=v2rg.....(i)

From triangle ABC,
sinθ=0.539.2=0.012tanθ=BCAC=0.539.220.52=0.012
We can see that values of sinθ and tanθ are very small.

For very small angle:
tanθθsinθ=BCAB...(ii)

From Eq.(i) and Eq. (ii)
v2rg=BCAB=hAB
v=h×r×gAB=0.5×800×9.839.2
or, v=10 m/s

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