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Option 4 : Bernoulli’s leminscate
Explanation:
The autogenous curve of an automobile” means the path traced by an automobile when turning freely is actually a ‘Lemniscate’.
It finds application in the design of transition curves for highways. In general, cubic spiral, cubic parabola, and lemniscate, all can be used in designing a transition curve. But lemniscate is preferred over the other two as
1) Its radius of curvature decreases gradually
2) The rate of increase of radius of curvature decreases at the end of the curve
Nonetheless, cubic spiral and cubic parabola find application in the design of transition curves in railways.
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