Statement I: A cyclist is moving on an unbanked road with a speed...

Statement I: A cyclist is moving on an unbanked road with a speed of $7km{h}^{- 1} and takes a sharp circular turn along a path of the radius of$ 2m $without reducing the speed. The static friction coefficient is$ 0 . 2 $. The cyclist will not slip and pass the curve \left(g = 9 . 8m{s}^{- 2}\right)$

Statement II : If the road is banked at an angle of $45 °$ , cyclist can cross the curve of $2m$ radius with the speed of $18 . 5km{h}^{- 1}$ without slipping. In the light of the above statements, choose the correct answer from the options given below.

Options

AStatement I is incorrect and statement II is correct
BStatement I is correct and statement II is
incorrect
CBoth statement I and statement II are false
DBoth statement I and statement II are true

Correct answer

D. Both statement I and statement II are true

Step-by-step solution

Statement I ${v}_\max = \sqrt{\muRg} = \sqrt{\left(0 . 2\right) \times 2 \times 9 . 8}$

${v}_\max = 1 . 97m{s}^{- 1}$

$7km{h}^{- 1} = 1 . 944m{s}^{- 1}$

Speed is lower than ${v}_\max$ , hence it can take safe
turn.

Statement II

${v}_\max = \sqrt{Rg \left[\dfrac{tan \theta + \mu}{1 - \mu tan \theta}\right]}$

$= \sqrt{2 \times 9 . 8\left[\dfrac{1 + 0 . 2}{1 - 0 . 2}\right]} = 5 . 42m{s}^{- 1}$

$18 . 5km{h}^{- 1} = 5 . 14m{s}^{- 1}$

Speed is lower than ${v}_\max$ , hence it can take safe turn.

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