The angle which the bicycle and its rider must make with the vertical when going round a curve of 8.1m radius at 9ms−1 is (Take g=10m/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 B45∘
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=8.1m,v=9ms−1 Putting values, tanθ=v2rg=9×98.1×10=1 θ=tan−1(1)=45∘