Question

A car turns on a road of radius \(300\,m\). Coefficient of friction = 0.3. Find maximum speed. (Take \(g=10\,m/s^2\))

• A. \(10\,m/s\)
• B. \(30\,m/s\)
• C. \(40\,m/s\)
• D. \(50\,m/s\)

Hint:

On flat roads, friction alone provides centripetal force. Always use \(v_{max} = \sqrt{\mu rg}\).

Answer 1

The Correct Option is B

Concept: When a vehicle moves on a flat circular road, friction provides the necessary centripetal force. \[ \text{Centripetal force} = \frac{mv^2}{r} \] Maximum frictional force: \[ f_{max} = \mu N = \mu mg \] At maximum speed: \[ \frac{mv^2}{r} = \mu mg \]

Step 1:Cancel common terms \[ \frac{v^2}{r} = \mu g \]

Step 2:Solve for \(v\) \[ v = \sqrt{\mu r g} \]

Step 3:Substitute values \[ v = \sqrt{0.3 \times 300 \times 10} \] \[ = \sqrt{900} \] \[ = 30\,m/s \]

Step 4:Interpretation This is the maximum safe speed. Beyond this speed, friction will be insufficient and the car may skid outward. Final Answer : 30\,m/s