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Question

The angle which the bicycle and its rider must make with the vertical when going round a curve of 8.1 m radius at 9 ms1 is (Take g=10 m/s2)

A
20
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B
45
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C
30
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D
60
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Solution

The correct option is B 45

The components of Normal reaction for cyclist need to satisfy the equation of dynamics i.e. supporting the weight & centripetal force.

So, we have
Nsinθ=mv2r.......(i)
Ncosθ=mg..........(ii)
On dividing (i) by (ii), we get
tanθ=v2rg
Here, r=8.1 m,v=9 ms1
Putting values,
tanθ=v2rg=9×98.1×10=1
θ=tan1(1)=45

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