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 10 % , the increase in the radius of curvature will be [Angle of banking and friction is unchanged in both the cases.]

Step-by-step solution

For road safety on a banked road, the velocity of the car has following scaling relation with respect to the curvature: v^2 R So, v^2=C R---(1) where C is a constant that involves the banking angle and friction. If the new velocity is v^ =1.1 v as 10 % higher speed, then v^ 2 =C R^ ---(2) where, R^ is the new radius of curvature due to safely. Now, take the ratio of equation (1) and (2) aligned & ( v^ v )^2= R^ R & (1.1)^2= R^ R & (1.1)^2-1 1 = R^ -R R aligned aligned & 0.21 1 = (R^ -R ) R & (R^ -R )=0.21 R=0.21 20