Banking Of Roads

Building on NCERT Class 11, Chapter 5 (Laws of Motion), when a road is banked so that friction is not required, the horizontal component of the normal reaction alone provides the centripetal force while its vertical component balances gravity. Combining these two equations gives the standard result tanθ = v² / (r g), where v is the optimum (design) speed. Substituting the given values, tanθ = 20² / (100 × 10) = 400 / 1000 = 0.4. This means the road is tilted just enough that gravity and the normal force together curve the car. Option 0.2 mistakenly uses v instead of v² in the numerator scaling. Option 0.8 doubles the correct value, perhaps from using 2v². Option 0.5 corresponds to a radius of 80 m, not the given 100 m. A deeper point is that this design speed is the only speed at which friction is completely unnecessary; at higher speeds friction must act down the slope and at lower speeds up the slope to keep the car on its circular path. The banking angle therefore depends only on the chosen design speed and radius, not on the mass of any particular vehicle. Plausibility check: tanθ being dimensionless and equal to 0.4 corresponds to a modest banking angle of about 22°, which is realistic for a highway curve, confirming the answer.