A2 Daily A Level Physics question
On a wet, flat roundabout a car just avoids skidding when it travels at speed v0 around a lane of radius R. The driver then moves to an inner lane of radius R/2. The tyre–road grip (maximum friction) is unchanged and must provide the inward force for the turn. To again be just at the limit of not skidding, what fraction of v0 should the new speed be?
Answer
The correct answer is C.
Correct: C — Reduced to about 0.71 of the original speed, 0.71 v0. At the skid limit, maximum friction provides the inward force, so the condition scales with v^2/r; therefore v ∝ √r, and halving r makes v → v0√(1/2) ≈ 0.71 v0. A confuses the scaling and assumes v ∝ r, giving 0.50 v0. B wrongly applies an extra power, as if v ∝ r^2, giving 0.25 v0. C follows v ∝ √r correctly for friction-limited circular motion. D ignores the radius dependence; while the maximum lateral acceleration is fixed by grip, the corresponding speed limit still varies as √r.