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Q.

Statement-I : A Cyclist is moving on an unbanked road with a speed of 7 kmh-1  and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2 the cyclist will not slip and pass the curve (g=9.8 m/s2)
Statement-II: If the road is banked at an angled of 450, cyclist can cross the curve of 2m radius with the speed of 18.5 kmh-1 without slipping.
In the light of the above statements, choose the correct answer from the options  given below.
 

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a

Statement I is Incorrect, statement II is Correct

b

Both statement I and statement II are false

c

Statement I is Correct and statement II is Incorrect

d

Both statement I and statement II are True

answer is D.

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Detailed Solution

On a horizontal ground

 vmax=μRg=0.2×2×9.8=1.97m/s=1.97×185=7.12km/hrSince, cyclist is riding at safer speed of 7 km/hr,Statement I is correct.

Statement -2

vmax=rgtanθ+μ1μtanθ=2×9.8×1.20.8=5.422m/s=19.5  km/hr

vmin=rgtanθμ1+μtanθ=2×9.8×0.81.2=3.615m/s=13.01km/hr

Since, speed of cyclist is between the safe limit of vmin and vmax,  Statement II is also correct.

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