1
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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 ms−1 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 ms−1 Putting values, tanθ=v2rg=9×98.1×10=1 θ=tan−1(1)=45∘

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