Sample 1Medium
A cross-section of a circular road of radius 160 m shows it banked at an angle θ with tan θ = 0.25. A car on it is drawn with its weight mg vertical and the normal reaction N perpendicular to the road surface; friction is taken as zero. Take g = 10 m/s². At what speed can the car go round the curve without skidding?
Show the answer
The answer is D.
With no friction, N sin θ provides mv²/r and N cos θ balances mg, so v² = rg tan θ = 160 × 10 × 0.25 = 400 and v = 20 m/s.
- A.
10 m/s gives v² = 100, a quarter of rg tan θ.
- B.
40 m/s gives v² = 1600, i.e. rg without the tan θ factor.
- C.
80 m/s does not satisfy v² = rg tan θ for any value given.
NCERT: Class 11 Physics, Chapter 4