Q1: If the length of a transition curve to be introduced between a straight and a circular curve of radius 500 m is 90 m, the maximum perpendicular offset for the transition curve, is

ANS:C - 2.70 m

Shift S = L^2/24R.
Perpendicular offset = 4 x Shift=4 x (L^2/24R).
= L^2/6R.
= 90x90/6* 500 = 2.7m. Perpendicular offset from a tangent to the junction of a transition curve and a circular curve is equal = 4 times the shift.
So, P=4s=4*(L^2/24R)=L^2/6R=90^2/(6*500)=2.70m. Y = x^3/6RL.
For maximum perpendicular offset x = L = 90 m.
So Y = 90^3/6*500*90 = 2.70 m.