First slide

Banking of road

Question

A curved road of 50 m in radius is banked to correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should be changed to

Easy

A

200 m
B

100 m
C

50 m
D

none of the above

Solution

$\tan θ = \frac{v^{2}}{rg} . Here \frac{v^{2}}{r} = constant$
or $\frac{{v_{1}}^{2}}{r_{1}} = \frac{{v_{2}}^{2}}{r_{2}}$ or $r_{2} = r_{1} \times \frac{{V_{2}}^{2}}{{V_{1}}^{2}}$
or $r_{2} = 50 \times \frac{{(2 V_{1})}^{2}}{{V_{1}}^{2}} = 50 \times 4 = 200 m$

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