Statement I: A cyclist on an unbanked road moves at 7 km/h around a curve of radius 2 m with µₛ=0.2; it will not slip. Statement II: If the same road is banked at 45°, the cyclist can take the 2 m radius curve at 18.5 km/h without slipping. Choose the correct option. (g=9.8 m/s²)
Options

Question

Statement I: A cyclist on an unbanked road moves at 7 km/h around a curve of radius 2 m with µₛ=0.2; it will not slip. Statement II: If the same road is banked at 45°, the cyclist can take the 2 m radius curve at 18.5 km/h without slipping. Choose the correct option. (g=9.8 m/s²)

Options

G1 Physics · Accepted Answer

For statement I, v=7/3.6≈1.94 m/s and required friction ratio v²/(rg)≈0.193<µₛ=0.2, so no slip. With banking at 45°, friction can extend the allowable speed range to include 18.5 km/h for the given µ. Hence both statements are true, option D.