[Images attached] What is the difference between C and D in question 30? Please

Question

[Images attached] What is the difference between C and D in question 30? Please explain in details

A car rounds a flat curve of radius R with a speed of v_0. The coefficient of friction between the tires and the road is mu. For the car not to slide on the road, which of the following statements must be true? (A) The car's speed v_0 cannot be greater than mu g R. (B) The car's speed v_0 cannot be less than mu g R (C) The radius R of the car's path cannot be greater than v_0^2/mu g (D) The radius R of the car's path cannot be less than v_0^2/mu g. (E) The centripetal acceleration must be less than g.

Explanation / Answer

When moving on a curve centripetal force = mvo^2/r which is provided by friction.

Sliding commences when centripetal force exceeds friction

mvo^2/r = umg

r = vo^2/ug

Hence answer is D

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