A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ___________ m/s.

Solution

Physics sir · 3 steps

On a level road friction alone gives the centripetal force, so the maximum speed goes as the square root of r.

1. Friction turns the car. On a level curve, static friction is the only horizontal force, so it supplies mv²/r. At the maximum speed, friction is at its limit μ mg.

   mvₘₐₓ²/r = μ mg ⇒ vₘₐₓ = √(μ r g)

2. Take the ratio. μ and g stay the same, so vₘₐₓ ∝ √r. That gives v₂/v₁ = √(r₂/r₁) = √(48/75) = √0.64 = 0.8.
3. So. v₂ = 0.8 × 30 = 24 m s⁻¹, so the answer is 24.

The common slip: 19.2. Taking vₘₐₓ proportional to r instead of √r gives 30 × 48/75 = 19.2, not 24.

The idea to keep. For a level curve, vₘₐₓ = √(μ r g), and the mass cancels. When only the radius changes, compare speeds using the square root of the radius ratio.

Answer from the NTA final answer key. Solution by PrepWiser.