Statement I : A cyclist is moving on an unbanked road with a speed of $7 \mathrm{kmh}^{-1}$ and takes a sharp circular turn along a path of radius of $2 \mathrm{~m}$ without reducing the speed. The static friction coefficient is $0.2$. The
cyclist will not slip and pass the curve $\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
Statement II : If the road is banked at an angle of $45^{\circ}$, cyclist can cross the curve of $2 \mathrm{~m}$ radius with the speed of $18.5 \mathrm{kmh}^{-1}$ without slipping.
In the light of the above statements, choose the correct answer from the options given below.
Correct Option: , 4
(4)
Statement I :
$\mathrm{v}_{\max }=\sqrt{\mu \mathrm{Rg}}=\sqrt{(0.2) \times 2 \times 9.8}$
$\mathrm{v}_{\max }=1.97 \mathrm{~m} / \mathrm{s}$
$7 \mathrm{~km} / \mathrm{h}=1.944 \mathrm{~m} / \mathrm{s}$
Speed is lower than $\mathrm{v}_{\max }$, hence it can take safe turn.
Statement II
$\mathrm{v}_{\max }=\sqrt{\mathrm{Rg}\left[\frac{\tan \theta+\mu}{1-\mu \tan \theta}\right]}$
$=\sqrt{2 \times 9.8\left[\frac{1+0.2}{1-0.2}\right]}=5.42 \mathrm{~m} / \mathrm{s}$
$18.5 \mathrm{~km} / \mathrm{h}=5.14 \mathrm{~m} / \mathrm{s}$
Speed is lower than $\mathbf{v}_{\max }$, hence it can take safe turn.
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