A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [take g = 10 ms⁻²]

Solution

Physics sir · 4 steps

On a flat curve, friction alone supplies the centripetal force, so set mv²/r = μ mg.

1. Who pulls inward. The road is horizontal, so there is no banking. The only force pointing toward the centre is static friction from the road on the tyres.
2. Limit of friction. Friction can be at most μ N = μ mg. At the maximum speed, the centripetal force needed equals this largest friction, and the mass cancels.

   mvₘₐₓ²/r = μ mg ⇒ vₘₐₓ = √(μ r g)

3. Put in numbers. vₘₐₓ = √(0.34 × 50 × 10) = √170 ≈ 13.04 m s⁻¹.
4. So. The maximum speed is about 13 m s⁻¹, which is option (b).

The idea to keep. For an unbanked turn, vₘₐₓ = √(μ r g), and it does not depend on the mass. Always take the square root at the end, because friction limits v², not v.

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