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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 mGiven 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=v2v′2=rgtanθr′gtanθ ⇒vv′=√rr′ ⇒r′=r×v′2v2 i.e r′=r×(12v10)2v2=1.44 r ∴r′=1.44×30 m=43.2 m

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