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Question

A bridge is in the form of a semi-circle of radius 10 m. The greatest speed with which a motorcycle can cross the bridge without leaving the ground at the highest point is (g=10 m/s2) (frictional force is negligibly small)
  1. 102 m/s
  2. 100 m/s 
  3. 10 m/s  
  4. 1010 m/s


Solution

The correct option is C 10 m/s  
By the FBD of the motor cycle at the top we get,

Here Fc is centrifugal force on motor cycle
Writing the force equation at the highest point we get,

N+Fc=mg
N+mv2R=mg
To achieve greatest speed, without leaving the ground at highest point,
N=0
mv2R=mg
v=Rg=10×10
=10 m/s

Hence option C is the correct answer

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