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Question

The maximum safe speed for a banked road is intended to be increased by 20%. If the angle of banking is not changed, then the radius of curvature of the road should be changed from 30 m to x m. The value of x is

A
53.2 m
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B
43.2 m
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C
62.4 m
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D
35.6 m
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Solution

The correct option is B 43.2 m
Given rold=r=30 m. Let rnew=r
and vnew=v
Then, v=v+20v100=12v10
We know the condition of banking
tanθ=v2rg
v2=rgtanθ....(i)

Putting old and new values in Eq. (i) and then dividing will yield:
v2oldv2new=v2v2=rgtanθrgtanθ
vv=rr
r=r×v2v2
i.e r=r×(12v10)2v2=1.44 r
r=1.44×30 m=43.2 m

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