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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 ms2) (frictional force is negligibly small).

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Solution

h=2TcosθrSg
[L]=[MT2][L][ML3][LT2]
=[MT2]ML1T2
=1L1=L
Dimensionally correct mv2 for not leave the surface.
mv2Rmg
v2R=g
V2=Rg=40×10=400
V=400=20 m/s.

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