A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by 20 % , without changing the angle of banking, the increase in the radius of curvature will be [Assume friction is same on the road]

Step-by-step solution

The maximum safe speed on a banked road with friction is given by v = rg + 1 - , where and remain constant. Denoting the constant term as K , this simplifies to v = rgK . Squaring both sides yields v^2 = rgK , showing v^2 is directly proportional to r . Given v₂ = 1.2v₁ and r₁ = 20 m , the proportionality gives v₂^2 v₁^2 = r₂ r₁ . Substituting v₂ = 1.2v₁ produces 1.44 = r₂ 20 . Solving, r₂ = 28.8 m and the increase is r = 8.8 m . 8.8 m