Question Detail
Question
A bridge is in the form of a semi-circle of radius 40 m. The greatest speed with which a motor cycle can cross the bridge without leaving the ground at the highest point is (g = 10 m/s²) (frictional force is negligibly small).
Correct Answer
Option B is the correct answer.
Detailed Explanation
At the highest point of the bridge (which is like a circular arc), the centripetal force is provided by the weight minus the normal force. To just lose contact, normal force = 0, so mg = mv²/r => v = √(gr) = √(10 × 40) = √400 = 20 m/s.
Hint
At the point of losing contact, the normal force becomes zero, so mg provides the centripetal force.