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NEETPhysicsMotion in Two Dimensions

A car is negotiating a flat, unbanked circular turn. For a turn of radius R , the maximum safe speed of the car without skidding is v . If the radius of the turn is increased to 4R while the coefficient of static friction remains the same, what will be the new maximum safe speed for the car?

Options

  1. A4v
  2. Bv 2
  3. C2v
  4. Dv 4

Correct answer

C. 2v

Step-by-step solution

The maximum safe speed for a car on a flat circular track is determined by the static friction providing the necessary centripetal force. Equating the maximum static friction to the required centripetal force: mv^2 R = mg Solving for v , we get: v = R g This shows that the maximum safe speed is directly proportional to the square root of the radius of the turn ( v R ). When the radius is increased to 4R , the new maximum safe speed v' is: v' = (4R) g = 2 R g = 2v . Answer: 2v

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