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 $2 m$ without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve $(g = 9.8 m / s^{2})$
Statement II: If the road is banked at an angle of $45^{\circ}$ , cyclist can cross the curve of 2 M 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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Both statement I and statement II are false

Statement I is incorrect and statement II is correct

Statement I is correct and statement II is incorrect

Both statement I and statement II are true

answer is D.

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Detailed Solution

Statement I:
   $v_{max} = \sqrt{μ Rg} = \sqrt{(0.2) \times 2 \times 9.8}$
   $v_{max} = 1.97 m / s$
   $7 km / h = 1.944 m / s$
Speed is lower than $v_{max}$ , hence it can take safe turn.
Statement II
   $\begin{array}{r} v_{max} = \sqrt{Rg [\frac{tan θ + μ}{1 - μ tan θ}]} \\ = \sqrt{2 \times 9.8 [\frac{1 + 0.2}{1 - 0.2}]} = 5.42 m / s \\ 18.5 km / h = 5.14 m / s \end{array}$
Speed is lower than $v_{max}$ , hence it can take safe turn.