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 30m to xm. The value of x is
A
53.2m
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B
43.2m
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C
62.4m
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D
35.6m
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Solution
The correct option is B43.2m Given rold=r=30m. 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=1.44r ∴r′=1.44×30m=43.2m